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?

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

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# 3 Answers

You must remember that log_{b}x=y implies b^{y} = x.

so log_{(x+2)}16 = 2 implies (x+2)^{2}=16.

Next (x+2)^{2 }= x^{2}+4x+4

So x^{2}+4x+4-16 = 0

Then x^{2}+4x-12 = 0.

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

Therefore (-6)(2) = -12

log_{(x+2)} 16 = 2

(x + 2)^{2} = 16

(x + 2)^{2} = (± 4)^{2}

x + 2 = ± 4

x_{1} + 2 = 4 ----> **x _{1} = 2**

x

_{2}+ 2 = - 4 ---->

**x**_{2}= - 6Hey 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 :)