1. ## logs as exponents

Hi;
I know that x^logx3 = 3 but what if the bases are not the same i.e. x^logy3 = ? for example, How do I solve these ones?

Thanks.

2. ## Re: logs as exponents

In general any logarithm, to any base, has the property that log(a^b)= blog(a). In particular log(x^logy(3))= log_y(3)log(x). That second logarithm can be to any base.

3. ## Re: logs as exponents

$$x^{\log_y z} = z^{\log_y x}$$

This is fairly easy to prove but does not simplify the problem much.