Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 826: 79

$x=2$

We have to find $x$ from tghe logarithmic equation: $$\log_{6}(\log_{2}x)=0.$$ We rewrite the equation in exponential form: $$\log_{a}b=c\Rightarrow b=a^c$$ $$\log_{2}x=6^0=1$$ Rewrite this equation in exponential form to find $x$: $$x=2^1=2$$ Check if the solution is valid: $$\log_6(\log_2 2)=\log_61=0\checkmark$$