Calculus Examples

$x = e^{t}$

Step 1

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

$e^{t} = x$

Step 2

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

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

Step 3

Expand the left side.

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Step 3.1

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

$t \ln (e) = \ln (x)$

Step 3.2

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

$t \cdot 1 = \ln (x)$

Step 3.3

Multiply $t$ by $1$ .

$t = \ln (x)$