Solve equations of the form:
ul
li(a^x=b )/li
li(e^ax+b = p )/li
li(\ln{(ax+b)} = q )[/li]/ul
[b]uExponential equations[/u]/b

(a^x=b \quad ) ((\log) both sides)

(\log{a^x}=\log{b} \quad ) (apply the power law)

(x\log{a}=\log{b} \quad ) (divide by (\log{a}))

(x=\dfrac{\log{b}}{\log{a}} \quad )

[b]uExponential equations with the natural base[/u]/b

(e^ax+b = p \quad ) ((\ln) both sides)

(\ln{e^ax+b}=\ln{p} \quad ) (cancel)

(ax+b=\ln{p} \quad ) (rearrange)

(x=\dfrac{\ln{p}-b}{a} \quad ) (rearrange)

[b]uNatural logarithmic equations[/u]/b

(\ln{(ax+b)} = q \quad ) ((e) to the power of both sides)

(e^\ln{(ax+b)}=e^{q} \quad ) (cancel)

(ax+b=e^q \quad ) (rearrange)

(x=\dfrac{e^q-b}{a} \quad ) (rearrange)