Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 338: 95

$10^{\frac{log3 log5}{log15}}\approx 1.921$

1. $log_5(x)+log_3(x)=1 \Longrightarrow \frac{log(x)}{log5}+\frac{log(x)}{log3}=1\Longrightarrow (\frac{1}{log5}+\frac{1}{log3})log(x)=1 \Longrightarrow log(x)=\frac{log3 log5}{log3+log5} \Longrightarrow x=10^{\frac{log3 log5}{log15}}\approx 1.921$ 2. Check, $x=10^{\frac{log3 log5}{log15}}$ fit(s).