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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 logbx=y  implies by = x.

so log(x+2)16 = 2 implies (x+2)2=16.

Next (x+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

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

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 :)