The only numbers you can plug into a logarithm are positive numbers not equal to 1. Negative numbers, and the number 0, aren’t acceptable arguments to plug into a logarithm, but why?
The reason has more to do with the base of the logarithm than with the argument of the logarithm. To understand why, we have to understand that logarithms are actually exponents. The base of a logarithm is also the base of a power function.
When you have a power function with base 0, the result of that power function is always going to be 0. In other words, there’s no exponent you can put on 0 that won’t give you back a value of 0. Or, put a different way, 0 raised to anything is always still 0. In the same way, 1 raised to anything is always still 1.
If you raise a negative number to a positive number that’s not an integer, but instead a fraction or a decimal, you might end up with a negative number underneath a square root. And as you know, unless we’re getting into imaginary numbers, we can’t deal with a negative number underneath a square root.
So 0, 1, and every negative number presents a potential problem as the base of a power function. And if those numbers can’t reliably be the base of a power function, then they also can’t reliably be the base of a logarithm.
For that reason, we only allow positive numbers other than 1 as the base of the logarithm. Then what we know is that, if the base of our power function is positive, it doesn’t matter what exponent we put on that base (it could be a positive number, a negative number, of 0), that power function is going to come out as a positive number.
So in summary, because the base can only be a positive number, that means the argument of the logarithm can only be a positive number. Which means that in order to protect our bases, we have to only allow positive arguments inside the logarithm.
Hope this helps!
No ,it is not possible for a logarithm to equal a negative number.
What is logarithm?A logarithmic is the power to which a number must be raised in order to get some other number.
For example, the logarithm base b of a number n is the number x that when b is raised to [tex]x^{th}[/tex] power, the resulting value in n i.e.
[tex]log_{b}n = x[/tex] ⇔ [tex]b^{x} =n[/tex]
No, it is possible for a logarithm to equal a negative number because logarithm function [tex]log_{a}(b) = n[/tex] is the inverse of the exponent function [tex]a^{n} =b[/tex] where the base a>0. Since, the base a raised to any exponent n is positive, the number b must be positive.
The logarithm of a negative number b is undefined.
Hence, it is not possible for a logarithm to equal a negative number.
Learn more about logarithm here:
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lauren wants to build a model airplane using a scale where 2 inches represents 15 feet. if the airplane is 75 feet long how many inches long should the model be?
Answer:
Its 10
Step-by-step explanation:
Explain your reasoning for your answer above.
I’ll give brainliest !!
Answer:
A
Step-by-step explanation:
The triangles are the same. Congruent is when all three sides are equal to each other on both triangles
PLEASE HELP
there are just as many square numbers as there are counting numbers. you can see that because you can match the squares up with the counting numbers, and you never run out of either. but doesn't it seem that there must be more counting numbers than squares since not every number is a square?
Answer:
i think its a yes
Step-by-step explanation:
Please help!! I'll give brainlist!
Answer:
-3/5
Step-by-step explanation:
-2/5+-1/5= -3/5
I used a calculator to ensure this answer was correct
The difference of the squares of two positive consecutive integers is 991. Find the integers.
Answer:
The numbers are 495 and 496.
Step-by-step explanation:
[tex](x+1)^{2} -x^{2} =991\\x^{2} +2x+1-x^{2} =991\\2x+1=991\\2x=990\\x=495[/tex]
is y=0.3x proportional
Answer:
yes
Step-by-step explanation:
what is 7,234,000,000,000,000 written in scientific notation helpp me plss!?
Answer:
7.234x10^14 that would be it in scientific notation
Joseph received a $20 gift card for downloading music. Each downloaded song costs $1.29. Explain how to write and solve an inequality that can be used to determine the number of songs that he can purchase.
Interpret the solution.
Answer:
Step-by-step explanation:
Answer:
Let x be the number of songs downloaded.
Each song is $1.29; the total cost would be found by multiplying the cost by the number of songs, or 1.29x.
This cannot be more than 20, so we set this less than or equal to 20:
1.29x ≤ 20.
To solve this, we divide both sides by 1.29:
≤ ;
x ≤15.5.
We cannot download half of a song, so we round this down to 15 (although the number rounds up mathematically, he would not have enough money to download 16 songs). This means he can download at most 15 songs.
Step-by-step explanation:
if you want the sample response then here: If x represents the number of downloads, you can write the inequality 1.29x ≤ 20. Solving the inequality, you find that x is less than or equal to about 15.5. Since he can’t download part of a song, Joseph can download 15 or fewer songs.
what is the y- int of 27x-9y = 27
The y-intercept is (0,-3)
The x-intercept is (1,0)
Answer:the y-intercept is (0,-3)
Step-by-step explanation:use the slope intercept form y=mx + b to find y intercept
Use the dropdown to complete the following inequality.
Answer:
>
Step-by-step explanation:
b is clearly negative
- - = +
so therefore, subtracting the negative will result in a larger answer than adding a small positive to a negative
Luis had 4 boxes of party favors. One full box contained 16 bags of favors and each bag had 5 items in it. What is the total number
items that Luis had in his possession?
O A. 360
B. 320
O C. 170
OD. 7.5
Find the circumference a circle with the diameter AB
A (-8,4) and B (4,-1)
Answer:
C = 13π ≈ 40.82 units
Step-by-step explanation:
C = 2 r π = d π
AB = [tex]\sqrt{(-8-4)^2 +(4+1)^2}[/tex] = 13 units
C = 13π ≈ 40.82 units ( π ≈ 3.14 )
2(4q+3)=4q-14
What is q?? HELP ASAP.
( Also show step by step please. )
What is the range of the function?
Answer:
B. 2, 6, 8
Step-by-step explanation:
I just learned this
0.7x9 pls answer idont know
Answer:
kuggtjbbbknh
Step-by-step explanation:
Answer:
6.3
Step-by-step explanation:
dont u have a calculator lol
Si sabemos que en una progresión aritmética el sexto término es 29 y la diferencia es 9. ¿Cuál es el primer término?
Answer:
-16
Step-by-step explanation:
De nada
Need a quick answer please
Answer:
X=10
MArk me brainliest
Step-by-step explanation:
Answer: The value of x is 10! How, you might ask, it is because it is reduced!
What is the value of the expression 3/8 divided by 2/5
Answer:
0.9375
Step-by-step explanation:
A fraction would probably be 15/16
write 600 as a product of a prime factor give your answer in index form
Answer:This is problems on common factors.
(a) 600 = 2 × 2 × 2 × 3 × 5 × 5
= 2³ˣ 3 ˣ 5²
(b) The highest common factors could be calculated using factors methods and the divisional methods.
Here we go.
(i) 600 = 2³ ˣ 3 ˣ 5²
1050 = 2 ˣ 3 ˣ 5² ˣ 7, the highest common factor HCF will be
HCT = 2 ˣ 3 ˣ 5²
= 150.
The divisional methods.
600) 1050 ( 1
- 600
------
450 ) 600 ( 1
- 450
------
150 ) 450 ( 3
- 450
------
000
So the answer is 150, the principle is that you continue to divide and subtract until you arrive at zero.
Answer = 150
If this is incorrect you should report my answer... Hope this was helpful... Stay safe and have a great weekend!!! :D
help, thank you so much!
Answer:
-2
Step-by-step explanation:
The average rate of change over [a, b] is simply the slope of the function over [a, b] because:
[tex]let\:g(x)=f'(x)\\\frac{\int\limits^b_a {g(x)} \, dx }{b-a} = \frac{f(b)-f(a)}{b-a}[/tex]
We have to find the avg ROC over [-3, 1] so the slope over the interval is
[tex]\frac{f(1)-f(-3)}{1-(-3)} = \frac{-6 - 2}{4} = \frac{-8}{4} = -2[/tex]
Brianna wants to use a pontoon boat on Saturday at the lake. She has exactly
$200 to spend on the boat rental. The rental is $30 an hour plus a $80 deposit.
How many hours can she rent the pontoon boat for? Create and solve an
equation for this situation.
Answer:
Step-by-step explanation:
She has 200
80 deposit - 200= 120 left to spend
80+30h=200
If she has 120 left to spend at 30 hr, she could have the boat for 4 hrs
80+30h=200 subtract 80 from both sides
30h=120 divide by the 30
h=4
Select a symbol to compare the numbers
A student wrote four statements during math class. Which statement contains an error?
Answer:
C
Step-by-step explanation:
The answer is C if you multiply (a)38×18=684
(b)46×16=736 (c)54×14=756 the question is 766 miles meaning that c is the wrong answer .i hope this was helpful.
Solve for x. Please answer correctly !!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!
Sum of the angles on a line is 180
[tex](6x + 4) + 90 + (5x - 2) = 180 \\ 11x + 92 = 180 \\ 11x = 180 - 92 \\ 11x = 88 \\ x = \frac{88}{11} \\ \\ x = 8[/tex]
Hope this will help....
for BOYS only, 12*12+13+78-90+56
Answer:
201
Step-by-step explanation:
Answer:
201
Step-by-step explanation:
Please answer it correctly I will mark you brainlist if you show ur work
Answer:
c. 6 and 8
Step-by-step explanation:
when x is 5 Y is between 6-8.
F(5) means x is 5.
Answer:
I an guessing BStep-by-step explanation:
According to the picture 5 is between 4 and 6 plus if you some math you and look at the line that is drawn you should get B to.Hope that helped if not sorry. ...Question 1 (1 point)
Sava
1 Sarah is saving for a new car. She has the following amount in her account $175 $225. $275
and $325 after weeks 1.2.3 and 4 respectively.
How much will she have after 10 weeks?
6
• 675
575
625
600
Question 21 point)
Answer:
am sorry
Step-by-step explanation:
i had to do it for more pts
325 × 10
3350
sorry am lost need help
Linear Equations with explanation plz
Solve the following inequality for n. Write your answer in simplest form.
1+4(-6n-4)<10n+4-n
Answer
n>- 19/33
1 Simplify 10n+4-n10n+4−n to 9n+49n+4.
1+4(-6n-4)<9n+41+4(−6n−4)<9n+4
2 Expand.
1-24n-16<9n+41−24n−16<9n+4
3 Simplify 1-24n-161−24n−16 to -24n-15−24n−15.
-24n-15<9n+4−24n−15<9n+4
4 Add 24n24n to both sides.
-15<9n+4+24n−15<9n+4+24n
5 Simplify 9n+4+24n9n+4+24n to 33n+433n+4.
-15<33n+4−15<33n+4
6 Subtract 44 from both sides.
-15-4<33n−15−4<33n
7 Simplify -15-4−15−4 to -19−19.
-19<33n−19<33n
8 Divide both sides by 3333.
-\frac{19}{33}<n−
33
19
<n
9 Switch sides.
n>-\frac{19}{33}n>−
33
19
Done
Which of the following fractions is expressed in simplified form?
Answer:
There aren't any fractions
Step-by-step explanation:
