Question
Solve for x in the logarithmic equation 10log(10123)=10x
10
log
(
10
123
)
=
10
𝑥
.(1 point)
Responses
x=123
𝑥
=
123
x equals 123
x=10123
𝑥
=
10
123
x equals 10 superscript 123 baseline
x=12310
𝑥
=
123
10
x equals 123 superscript 10 baseline
x=10
10
log
(
10
123
)
=
10
𝑥
.(1 point)
Responses
x=123
𝑥
=
123
x equals 123
x=10123
𝑥
=
10
123
x equals 10 superscript 123 baseline
x=12310
𝑥
=
123
10
x equals 123 superscript 10 baseline
x=10
Answers
GPT-4o mini
To solve the equation \( 10 \log(10^{123}) = 10x \), we can first simplify the left side.
Using the property of logarithms that states \( \log(a^b) = b \log(a) \), we can rewrite \( \log(10^{123}) \):
\[
\log(10^{123}) = 123 \log(10)
\]
Since \( \log(10) = 1 \):
\[
\log(10^{123}) = 123 \cdot 1 = 123
\]
Now, we can substitute this back into the equation:
\[
10 \log(10^{123}) = 10 \cdot 123 = 1230
\]
So our equation now looks like:
\[
1230 = 10x
\]
Now, we can solve for \( x \):
\[
x = \frac{1230}{10} = 123
\]
Thus, the solution for \( x \) is:
\[
\boxed{123}
\]
Using the property of logarithms that states \( \log(a^b) = b \log(a) \), we can rewrite \( \log(10^{123}) \):
\[
\log(10^{123}) = 123 \log(10)
\]
Since \( \log(10) = 1 \):
\[
\log(10^{123}) = 123 \cdot 1 = 123
\]
Now, we can substitute this back into the equation:
\[
10 \log(10^{123}) = 10 \cdot 123 = 1230
\]
So our equation now looks like:
\[
1230 = 10x
\]
Now, we can solve for \( x \):
\[
x = \frac{1230}{10} = 123
\]
Thus, the solution for \( x \) is:
\[
\boxed{123}
\]