Can someone show how to this question.

Question

Loga(x+3) + Loga(x-3) = 3

I don't know if I'm typing this correctly the a is the base.

So, I'm thinking,

Loga((x+3)(x-3)) = 3

(x+3)(x-3) = 3^a
x^2 - 9 = 3^a,
x^2 = 3^a + 9
x = sqrt(3^a + 9)

but now I'm stuck, I don't know how to proceed. I don't know if this is the answer...

Answer 1

You are mixing up 3^a and a^3
The base of the logarithm (a) is what gwets raised to a power (3, in this case).

loga[(x+3)(x-3)] = 3
loga(x^2-9) = 3
a^3 = x^2-9
x = sqrt(a^3 +9)

Answer 2

Thanks... got it...