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

Question

.(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:

\[ \boxed{24} \]