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I find myself trying to work out something where the formula is something to the power of two things multiplied equals something else. A bit like this:

$a^{(b.c)}=d$

My math skill is insufficient for me to work out how to make one of the exponents the subject. I'm after:

b = some function of everything else.

I tried applying the b root to both sides and just twisted myself up into a mess that made no sense.

Would someone kindly explain like I'm twelve, the steps I need to take to make an exponent (b, in my case) the subject of the expression?

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1 Answer

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Take logarithms of both sides$$a^{bc}=d \implies bc\log(a)=\log(d)\implies b=\frac 1 c \frac{\log(d) } {\log(a) }$$

For sure, as @Jeanba commented, this implies that the arguments of the logarithmic function must be strictly greater than zero.

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