The solution set of the equation $\log _ { 3 } \left( \log _ { 3 } x \right) = 1$ is

A){3}
B){-3}
C){9}
D){-9}
E){27}

Question

The solution set of the equation $\log _ { 3 } \left( \log _ { 3 } x \right) = 1$ is

A){3}
B){-3}
C){9}
D){-9}
E){27}

Quizplus · Accepted Answer

The equation $\log _ { 3 } \left( \log _ { 3 } x \right) = 1$ can be solved by working from the outside in. First, we rewrite the equation as $\log _ { 3 } y = 1$, where $y = \log _ { 3 } x$. Solving for $y$, we get $y = 3^1 = 3$. This means $\log _ { 3 } x = 3$, which implies $x = 3^3 = 27$. Therefore, the solution set is {27}.

The Solution Set of the Equation log⁡3(log⁡3x)=1\log _ { 3 } \left( \log _ { 3 } x \right) = 1log3​(log3​x)=1

The Solution Set of the Equation $\log _ { 3 } \left( \log _ { 3 } x \right) = 1$