Question

Solve for x in the logarithmic equation 10^log(10^24)=10^x
.(1 point)
Responses

x=24
x equals 24

x=10
x equals 10

x=10^24
x equals 10 superscript 24 baseline

x=24^10

Answer 1

To solve the equation \( 10^{\log(10^{24})} = 10^x \), we can simplify the left side first.

We know that:

\[
\log(10^{24}) = 24
\]

Then, substituting this back into the equation gives:

\[
10^{\log(10^{24})} = 10^{24}
\]

So, we can rewrite the equation as:

\[
10^{24} = 10^x
\]

Since the bases are the same, we can equate the exponents:

\[
x = 24
\]

Thus, the solution is:

\[
\boxed{24}
\]