Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 475: 70

$x=200.8$

Recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition to our equation, we get: $10^3=5x-4$ $10^3+4=5x$ $\frac{1}{5}(10^3+4)=x$ $x=\frac{1004}{5}=200.8$ We confirm that the answer works: $\log_{10} (5\cdot200.8-4)=3$ $\log_{10} (1004-4)=3$ $\log_{10} (1000)=3$ $3=3$