Precalculus Examples

$\ln (\ln (x)) = 1.5$

Step 1

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (\ln (x))} = e^{1.5}$

Step 2

Rewrite $\ln (\ln (x)) = 1.5$ 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 $b^{y} = x$ .

$e^{1.5} = \ln (x)$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $\ln (x) = e^{1.5}$ .

$\ln (x) = e^{1.5}$

Step 3.2

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (x)} = e^{e^{1.5}}$

Step 3.3

Rewrite $\ln (x) = e^{1.5}$ 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 $b^{y} = x$ .

$e^{e^{1.5}} = x$

Step 3.4

Rewrite the equation as $x = e^{e^{1.5}}$ .

$x = e^{e^{1.5}}$

Step 4