# Math

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Solve for x.

log3(x+7)=2-log3(x-1)

Write the exact answer using base-10 logarithms.

• Math -

log3(x+7)=2-log3(x-1)
log3(x+7) + log3(x-1) = 2
log3 [(x+7)/(x-1)] = 2
(x+7)(x-1) = 3^2
x^2 + 6x - 7 = 9
x^2 + 6x - 16 = 0
(x+8)(x-2) = 0
x = -8 or x = 2

but x=-8 would make log3(x+7) undefined, so

x = 2

( why would it ask to use base 10 logs ????)

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