Question

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

x = 1024
x = 10 to the 24th power

x = 2410
x = 2410

x = 24
x = 24

x = 10

Answer 1

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

1. We know that \( \log(10^{24}) = 24 \) (since \( \log_{10}(10^a) = a \)).
2. Thus, we can rewrite the equation as:

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

So, the equation becomes:

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

3. Since the bases are the same, we can set the exponents equal to each other:

\[
x = 24
\]

The correct answer is:

**x = 24**