how do i solve these log equations, please.?

Question

log subscript a (a^2*a^3)

log subscript 8 (8^k)

how do i find the inverse of log subscript 4 (x) ?

thanks for the help.

Answer 1

First one:
first off: a^2 * a^3 = a^5, try using a = 10 and you'll see.
next: log(base-a) of a^5 = 5, since
"log(base-Y) of X = what power of Y is equal to X"

2nd one:
for same reasons... = k

3rd one:
well, given the above, the inv-log (base Y) of X = Y^X,
so inv-log (base 4) of X = 4^X

Answer 2

log (base a) of (a^2*a^3)=
log (base a) of (a^5)=
5 log (base a) of (a)=
5

log (base 8) of (8^k) =
k log (base *) of (8)=
k

log (base 4) of (x)=
log (x)/ log (4)
so the inverse is
log (4)/ log (x) =
log (base x) of (4)