Solve for x natural log of natural log of x-1=5

$\ln (\ln (x - 1)) = 5$

Step 1

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

$e^{\ln (\ln (x - 1))} = e^{5}$

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 $b^{y} = x$ .

$e^{5} = \ln (x - 1)$

Step 3

Solve for $x$ .

Rewrite the equation as $\ln (x - 1) = e^{5}$ .

$\ln (x - 1) = e^{5}$

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

$e^{\ln (x - 1)} = e^{e^{5}}$

Rewrite $\ln (x - 1) = e^{5}$ 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 $b^{y} = x$ .

$e^{e^{5}} = x - 1$

Solve for $x$ .

Rewrite the equation as $x - 1 = e^{e^{5}}$ .

$x - 1 = e^{e^{5}}$

Add $1$ to both sides of the equation.

$x = e^{e^{5}} + 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = e^{e^{5}} + 1$

Decimal Form:

$x = 2.85112356 \cdot 10^{64}$

Solve for x natural log of natural log of x-1=5

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