Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 338: 96

$10^{\frac{3log2 log6}{log12}}\approx 4.479$

1. $log_2(x)+log_6(x)=3 \Longrightarrow \frac{log(x)}{log2}+\frac{log(x)}{log6}=3\Longrightarrow (\frac{1}{log2}+\frac{1}{log6})log(x)=3 \Longrightarrow log(x)=\frac{3log2 log6}{log12} \Longrightarrow x=10^{\frac{3log2 log6}{log12}}\approx 4.479$ 2. Check, $x=10^{\frac{3log2 log6}{log12}}$ fit(s).