How can I rearrange ($a$ * $b$)^$c$=$d$ to make $c$ the subject

Is it at all possible to rearrange this equation to make c the subject. My dad and I believe it is possible but I am unable to correctly rearrange for c.

This is done using your basic log rules. The main rule to use is: $$y=log_b(x)=>x=b^y$$

$$(a*b)^c=d$$ $$clog(ab)=log(d)$$ $$c=\frac{log(d)}{log(ab)}$$ $$(c=log_{ab}(d))$$
Logarithms are the inverses of exponents. If $\log_x(y)=z$, then $x^z = y$; that's the definition of a logarithm.