Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 474: 56

$x=3$

We are asked to solve: $\log_{7}{343}=x$ Recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition to our equation (with $b=7, y=x, x=343$), we get: $7^x=343$ Because we know that $7^3=343$: $x=3$ We confirm that the answer works: $\log_{7}{343}=3$ $7^3=343$ $343=343$