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

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### 3 Answers

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.**

We need to solve: log(8) (y+2)=3

log(8) (y+2)=3

=> y + 2 = 8^3 = 512

=> y = 512 - 2

=> y = 510

**The solution of the equation is y = 510**

The first action is to impose constraints of existence of logarithms:

y + 2> 0

y > -2

The solution of the equation must be located in the range (-2 ; +infinite), for the logarithm to exist.

We'll solve the equation taking antilogarithm:

y + 2 = 8^3

y + 2 = 512

y = 512 - 2

y = 510

**Since y = 510 is in the interval of admissible values for y, then y = 510 is the solution of the given equation.**