Im learning logs right now and Im a bit confused on one of the identies.

Can you please clarify this?

\(\log_c b = \frac{\log_a b}{\log_a c}\)

What is a?

Is it anything we want, is it 10?

Thanks

Guest Dec 26, 2020

#2**+1 **

I think this is often referred to as the base change identity

log_{c }b = x means c^{x} = b

c^{x}=b now take log_{a} of both sides

x log_{a} c = log_{a }b now divide both sides by log_{a} c

x = log_{a} b / log_{a} c see that red equation above? x = log_{c} b ....sub that in for x

log_{c} b = log_{a} b_{ }/ log_{a} c which is your identity !

Guest Dec 26, 2020