Question

Solve for x in the logarithmic equation 10 ^log(10^5)=10x

Answer 1

To solve the equation \( 10^{\log(10^5)} = 10x \), we can simplify the left side using the properties of logarithms.

First, recall that \( \log(10^5) = 5 \) because the logarithm base 10 of \( 10^5 \) is simply the exponent itself. Thus, we rewrite the equation:

\[
10^{\log(10^5)} = 10^5
\]

So the equation becomes:

\[
10^5 = 10x
\]

Next, we can divide both sides of the equation by \( 10 \):

\[
10^5 / 10 = x
\]

This simplifies to:

\[
10^{5-1} = x
\]
\[
10^4 = x
\]

Thus, the solution for \( x \) is:

\[
\boxed{10000}
\]