Solve for x, how?

Question

5log8X=log8 16

Answer 1

5*log_8(x) = log_8(16)
log_8(x^5) = log_8(16)
x^5 = 16
x = 16^(1/5)
x = 2^(4/5)

I assume log8 means "log base 8," which is better written as log_8. Remember that a*log(b) = log(b^a) and that log(a) = log(b) ==> a = b.

Answer 2

5*log8 X = log8 16
log8 X^5 = log8 16
X^5 = 16
X = 16^(1/5)

Answer 3

Since you have log (base 8) on both sides of the equal sign it would be great if you had:

log (base 8) (something) = log (base 8) (something)

because then you know the two "something"s have to be equal. (... just like if you have the sqaure root of something is equal to the square root of something then the two "something"s have to be equal)

Anyway, you almost have log (base 8) (something) = log (base 8) (something). All you have to do is move the "5*". Do you know the rule/property that says:
5*log (base 8) (x) = log (base 8) (x^5)?

So ...
5*log (base 8) (x) = log (base 8) (16)
log (base 8) (x^5) = log (base 8) (16)

Now you know the two "something"s are equal ...

x^5 = 16
x = fifth root (16) .... or 16^(1/5)
which is approximately equal to 1.7411