Exponential equations

An exponential equation has the unknown in the exponent. The calculator solves the form:

$a\cdot b^{\,x}=c$

Method: divide both sides by $a$, then take the logarithm — which pulls the unknown down from the exponent:

$x=\log_b\!\frac{c}{a}=\frac{\ln(c/a)}{\ln b}$

Conditions: the base $b>0$ and $b\neq1$, and the ratio $c/a>0$ (otherwise the equation has no real solution, because an exponential function takes only positive values).