how do you solve for the possible answers for log 16 base x+2 is equal to 2?

Question

how do you solve for the possible answers for log 16 base x+2 is equal to 2? What is the product of all possible solutions?

Answer 1

You must remember that log_bx=y  implies b^y = x.

so log_(x+2)16 = 2 implies (x+2)²=16.

Next (x+2)² = x²+4x+4

So x²+4x+4-16 = 0

Then x²+4x-12 = 0.

Using the quadratic formula (-b+√b²-4ac) / 2a  gives us -6 and +2.

Therefore (-6)(2) = -12

Answer 2

log_(x+2) 16 = 2

(x + 2)² = 16
(x + 2)² = (± 4)²
x + 2 = ± 4
x₁ + 2 = 4   ----> x₁ = 2
x₂ + 2 = - 4 ----> x₂ = - 6

Answer 3

Hey Folami -- here's a way to recall how "logs" work ... log 100 (base 10) = 2 translates to (base 10)^2 = 100 ... So, log 16 (base x+2) = 2 says (x+2)^2 = 16 ... what squared is 16?? ==> plus / minus 4 ... x= 2, -6 <== Best regards :)