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- #1

http://puu.sh/2Lbb1.png

The answer is x = -1.70951.

how do we get there? please explain everystep. thanks :3

****someone made it this far, idk if it is the correct path:

log2 (2^(x-1)+3^(x+1)) = 2x - log2 (3^x)

log2 (2^(x-1)+3^(x+1)) + log2 (3^x) = 2x

because of the rule log(m) + log(n) = log(mn),

log2 ((2^(x-1)+3^(x+1))*(3^x) = 2x

log2 ((2^(x-1)+3^(x+1))*(3^x) = 2x

log ((2^(x-1)+3^(x+1))*(3^x) / log 2 = 2x

log ((2^(x-1)+3^(x+1))*(3^x) = 2x * log 2

log ((2^(x-1)+3^(x+1))*(3^x) = log 2^(2x)

equate the logs

(2^(x-1) + 3^(x+1))*(3^x) = 2^(2x)

2^(x-1) * 3^x + 3^(2x+1) = 2^(2x)

3^(2x+1) = 2^(2x) - 2^(x-1) * 3^x