Algebra Examples

$e^{b} = 46$

Step 1

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

$\ln (e^{b}) = \ln (46)$

Step 2

Expand the left side.

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Step 2.1

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

$b \ln (e) = \ln (46)$

Step 2.2

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

$b \cdot 1 = \ln (46)$

Step 2.3

Multiply $b$ by $1$ .

$b = \ln (46)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$b = \ln (46)$

Decimal Form:

$b = 3.82864139 \dots$