If log8 (y+2)=3, then what is y?

log8 (y+2) = 3

First we will
determine the domain.

==> y+ 2 >
0

==> y > -2
...........(1)

First we will rewrite using the exponent
form.

==> y+ 2=
8^3

==> y+ 2 = 512

Now
we will subtract 2 from both sides.

==> y = 512 - 2=
510 > -2 . ( satisfies the
domain.)

Then the value of y that satisfies
the logarithm equation is y= 510.