Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 476: 85

$x=333$

Recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition, we get: $10^3=1+3x$ $1000=1+3x$ $1000-1=3x$ $999=3x$ $\dfrac{999}{3}=x$ $333=x$ We check the answer: $\log_{10} (1+3\cdot 333)=3$ $\log_{10} (1000)=3$ $\log_{10} (10^3)=3$ $3=3$