Trigonometry Examples

$\log_{2} (\log_{3} (x)) = 2$

Step 1

Rewrite $\log_{2} (\log_{3} (x)) = 2$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$2^{2} = \log_{3} (x)$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $\log_{3} (x) = 2^{2}$ .

$\log_{3} (x) = 2^{2}$

Step 2.2

Rewrite $\log_{3} (x) = 2^{2}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$3^{2^{2}} = x$

Step 2.3

Solve for $x$ .

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Step 2.3.1

Rewrite the equation as $x = 3^{2^{2}}$ .

$x = 3^{2^{2}}$

Step 2.3.2

Simplify $3^{2^{2}}$ .

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Step 2.3.2.1

Raise $2$ to the power of $2$ .

$x = 3^{4}$

Step 2.3.2.2

Raise $3$ to the power of $4$ .

$x = 81$