Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 474: 53

$x=3$

We are asked to solve: $\log_{4}{64}=x$ Recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition to our equation (with $b=4, y=x, x=64$), we get: $4^x=64$ Because we know that $4^3=64$: $x=3$ We confirm that the answer works: $\log_{4}{64}=3$ $4^3=64$ $64=64$