Finding the power

[jedidia]

This is probably a dumb question, but I can't find the answer by googling.

If a^x = b, and I have a and b, what's the operation to find x? (I assume there is one?)

 

[GLS]

Logarithm?

 

[jedidia]

Indeed. If only I could keep in my head what that thing does, it's like I'm discovering it anew every time I need it.
so x = b log(a). If that's even the way it's written.

 

[GLS]

Indeed. If only I could keep in my head what that thing does, it's like I'm deiscovering it anew every time I need it.
so x = b log(a). If that's even the way it's written.

"a^x = b" equals "loga (b) = x", but because calculators (or papel tables) don't have logarithm of base "a" you can't calculate it directly. But, you can do the ratio of 2 know logarithms of any base, which will give what you want: you can use base 10 (usually labeled log10) or the natural logarithm of base "e" (labeled ln)
log10 (b) / log10 (a) = ln (b) / ln (a) = x