Solve for x e^(0.12x)=100

$e^{0.12 x} = 100$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{0.12 x}) = \ln (100)$

Expand the left side.

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Expand $\ln (e^{0.12 x})$ by moving $0.12 x$ outside the logarithm.

$0.12 x \ln (e) = \ln (100)$

The natural logarithm of $e$ is $1$ .

$0.12 x \cdot 1 = \ln (100)$

Multiply $0.12$ by $1$ .

$0.12 x = \ln (100)$

Divide each term by $0.12$ and simplify.

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Divide each term in $0.12 x = \ln (100)$ by $0.12$ .

$\frac{0.12 x}{0.12} = \frac{\ln (100)}{0.12}$

Cancel the common factor of $0.12$ .

$x = \frac{\ln (100)}{0.12}$

Simplify $\frac{\ln (100)}{0.12}$ .

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Rewrite.

$x = \frac{4.60517018}{0.12}$

Divide $4.60517018$ by $0.12$ .

$x = 38.37641821$

Solve for x e^(0.12x)=100

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