log[5](X+14)-log[5](X-10)=2

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original expression.
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1 Answer

log5(X+14)-log5(X-10)=2,

log5[(X+14)/(X-10)]=2,

(X+14)/(X-10)=52=25,

X+14=25X-250,

264=24X, X=264/24=11.

CHECK: log5(X+14)-log5(X-10)=log5(25)-log(1)=log5(25)=2. Solution X=11 checks out.

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