Solve for b 10^b=91

$10^{b} = 91$

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{b}) = \log (91)$

Expand the left side.

Expand $\log (10^{b})$ by moving $b$ outside the logarithm.

$b \log (10) = \log (91)$

Logarithm base $10$ of $10$ is $1$ .

$b \cdot 1 = \log (91)$

Multiply $b$ by $1$ .

$b = \log (91)$

The result can be shown in multiple forms.

Exact Form:

$b = \log (91)$

Decimal Form:

$b = 1.95904139 \dots$