Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 475: 75

$x=\dfrac{343}{3}\approx 114.3333$

Recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition to our equation, we get: $7^3=3x$ $343=3x$ $\dfrac{343}{3}=x$ $x\approx 114.3333$ We confirm that the answer works: $\log_{7} (3\cdot114.3333)=3$ $\log_{7} (343)=3$ $3=3$