Thread: Logarithms and patterns

Here is a quetion I couldn't solve.

Let loga (x) = c and logb (x) = d.
Find the general statement that expresses logab (x), in terms of c and d.

I would appreciate your help, thanks a lot,
Amine

loga (x) = c

logb (x) = d

logab (x) = ?


a^c = x and b^d = x

a = x ^ (1/c) and b = x ^ (1/d)

ab = x^ 1/c x ^ 1/d

= x ^ (d+c/cd)

logab (x) = d+c / cd


humm i might have flipped something

Hello, rubix!

Ya done good!

I'll put it in LaTex . . .

Multiply [1] and [2]: .


Therefore: .

Good work!

thnx for conforming Soroban...and thnx for nice well formatted answe.

cheers.

Thanks a lot for your help!