Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 475: 67

$x=10$

We are asked to solve: $\log_{10} x^2=2$ Recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition to our equation, we get: $10^2=x^2$ $x=\sqrt{10^2}$ $x=10$ We confirm that the answer works: $\log_{10} 10^2=2$ $2\log_{10} 10=2$ $2(1)=2$ $2=2$