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

.(1 point)

3 answers

To solve the equation \( 10^{\log(10^5)} = 10x \), we can start by simplifying the left-hand side.

We know that:

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

because the logarithm base 10 of \( 10^5 \) is simply the exponent. Thus we can rewrite the left-hand side:

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

So now our equation becomes:

\[ 10^5 = 10x \]

Next, we can divide both sides by 10:

\[ 10^5 / 10 = x \]

which simplifies to:

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

Thus,

\[ 10^4 = x \]

Finally, we can express \( x \) in terms of a numerical value:

\[ x = 10000 \]

So the solution is:

\[ \boxed{10000} \]

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