Meaning of exponent in logarithm?

Question

I have this particular difficulty : $$\log_b^a(c)=x$$
I know it is different from power of base $\log_{b^a}(c)=x$, but what does it actually mean?

The actual question that i got in paper was
Find value of $$\sqrt{\log_{0.5}^2 8}$$
And its answer was given as $3$.

Answer 1

The exponent is a power, so you should read $\log_b^a(c)=x$ as $(\log_b(c))^a=x$ In your specific case, $\log_{0.5}8=-3$, so when you square that you get $9$ and when you take the square root you get get $3$.

Answer 2

Well that pretty much means $$(\log_{b}(c))^a$$ In you case, it simplifies to $$\sqrt{(\log_{0.5}{8})^2} = |\log_{0.5}{8}| = |-3| = 3$$