Solve for b e^b=46

$e^{b} = 46$

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.

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

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

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

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

Multiply $b$ by $1$ .

$b = \ln (46)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$b = \ln (46)$

Decimal Form:

$b = 3.82864139 \dots$