Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 473: 35

$x=10000$

Subtract $4$ from each side: $\log_{10} x+4=8$ $\log_{10} x=8-4$ $\log_{10} x=4$ Recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition to our equation (with $b=10, y=4, x=x$), we get: $10^4=x$ $x=10000$ We confirm that the answer works: $\log_{10} 10000+4=8$ $\log_{10}(10^4)+4=8$ $4+4=8$ $8=8$