Using the power rule of logarithms, we can rewrite log x^4 as 4 * log x.
Since log x = 0.25, we can substitute this value into the expression: 4 * 0.25 = 1. So, log x^4 = 1.
If logx=0.25
, what is log x^4? Rewrite using the power rule, then evaluate. (1 point)
11 answers
If log h=3/5
, what is log h^3
? Rewrite using the power rule, then evaluate. Write your answer as a fraction. (1 point)
, what is log h^3
? Rewrite using the power rule, then evaluate. Write your answer as a fraction. (1 point)
Using the power rule of logarithms, we can rewrite log h^3 as 3 * log h.
Since log h = 3/5, we can substitute this value into the expression: 3 * (3/5) = 9/5.
So, log h^3 = 9/5.
Since log h = 3/5, we can substitute this value into the expression: 3 * (3/5) = 9/5.
So, log h^3 = 9/5.
Evaluate log100−−−√3
.(1 point)
log100−−−√3=
.(1 point)
log100−−−√3=
To evaluate log100√3, we can rewrite it as log100(3)^(1/2).
Using the property of logarithms, loga(b^c) = c * loga(b), we can rewrite the expression as (1/2) * log100(3).
Since 100 can be expressed as 10^2, we have log100(3) = log10^2(3).
Using the property loga(b^c) = c * loga(b), this can be further simplified to 2 * log10(3).
Since log10(3) is not a common logarithm, we use a calculator to find that log10(3) ≈ 0.477121255.
Therefore, log100√3 ≈ 2 * 0.477121255 = 0.954242509.
Using the property of logarithms, loga(b^c) = c * loga(b), we can rewrite the expression as (1/2) * log100(3).
Since 100 can be expressed as 10^2, we have log100(3) = log10^2(3).
Using the property loga(b^c) = c * loga(b), this can be further simplified to 2 * log10(3).
Since log10(3) is not a common logarithm, we use a calculator to find that log10(3) ≈ 0.477121255.
Therefore, log100√3 ≈ 2 * 0.477121255 = 0.954242509.
Evaluate log
.(1 point)
log 3√100. (1 point)
log 3√100 = ?
.(1 point)
log 3√100. (1 point)
log 3√100 = ?
To evaluate log 3√100, we can rewrite it as log(100^(1/3)).
Using the property of logarithms, log(a^b) = b * log(a), we can further simplify it to (1/3) * log(100).
Since log(100) can be expressed as log(10^2), we have (1/3) * log(10^2).
Using the property log(a^b) = b * log(a), this can be simplified to (1/3) * 2 * log(10).
The logarithm base 10 of 10 is equal to 1, so we have (1/3) * 2 * 1 = 2/3.
Therefore, log 3√100 = 2/3.
Using the property of logarithms, log(a^b) = b * log(a), we can further simplify it to (1/3) * log(100).
Since log(100) can be expressed as log(10^2), we have (1/3) * log(10^2).
Using the property log(a^b) = b * log(a), this can be simplified to (1/3) * 2 * log(10).
The logarithm base 10 of 10 is equal to 1, so we have (1/3) * 2 * 1 = 2/3.
Therefore, log 3√100 = 2/3.
Find the value of log 0.00001. (1 point)
log 0.00001 = ?
log 0.00001 = ?
The value of log 0.00001 can be calculated using the base 10 logarithm.
log 0.00001 = log(1/100000) = log(10^(-5)).
Using the logarithm property log(a^b) = b * log(a), we can rewrite it as -5 * log(10).
The logarithm base 10 of 10 is equal to 1, so we have -5 * 1 = -5.
Therefore, log 0.00001 = -5.
log 0.00001 = log(1/100000) = log(10^(-5)).
Using the logarithm property log(a^b) = b * log(a), we can rewrite it as -5 * log(10).
The logarithm base 10 of 10 is equal to 1, so we have -5 * 1 = -5.
Therefore, log 0.00001 = -5.
Which of the following expressions correctly expands log 16 to its simplest form? (1 point)
Responses
16 log 1
4 log 2
log 8 ⋅ log 2
2 log 8
Responses
16 log 1
4 log 2
log 8 ⋅ log 2
2 log 8
The correct expression to expand log 16 to its simplest form is 2 log 8.
We can rewrite 16 as 2^4, and using the exponent property log(a^b) = b * log(a), we have:
log 16 = log(2^4) = 4 log 2 = 2 log 8.
Therefore, the correct expression is 2 log 8.
We can rewrite 16 as 2^4, and using the exponent property log(a^b) = b * log(a), we have:
log 16 = log(2^4) = 4 log 2 = 2 log 8.
Therefore, the correct expression is 2 log 8.
1 answer