Question

evaluate the expression without using a calculator.
$10^{log 10}$
$10^{log 10} = \square$

Explanation:

Step1: Recall the inverse property of logarithms

The inverse property of logarithms states that for any positive number \( x \), \( 10^{\log x}=x \). This is because the logarithm base 10 (denoted as \( \log \)) and the exponential function with base 10 are inverse functions of each other.

Step2: Apply the inverse property

In the given expression \( 10^{\log 10} \), we can apply the inverse property of logarithms. Here, \( x = 10 \). So by the property \( 10^{\log x}=x \), when \( x = 10 \), we have \( 10^{\log 10}=10 \).

Answer:

\( 10 \)