What is the answer to log_{x-1}(x+5)=2 ?

The answer to log_{x-1}(x+5)=2 is x=4

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log_{x-1}(x+5)=2

lo g_{x - 1} (x + 5) = 2

x = 4

Solution steps

lo g_{x - 1} (x + 5) = 2

Apply log rules

\frac{ln ( x + 5 )}{ln ( x - 1 )} = 2

Multiply both sides by

ln (x - 1)

\frac{ln ( x + 5 )}{ln ( x - 1 )} ln (x - 1) = 2 ln (x - 1)

Simplify

ln (x + 5) = 2 ln (x - 1)

Apply log rules

x + 5 = (x - 1)^{2}

Solve

x + 5 = (x - 1)^{2} : x = 4, x = - 1

x = 4, x = - 1

Verify Solutions:

x = 4

True

, x = - 1

False

The solution is

x = 4

lo g_{3} (2 - x) = 3

lo g_{x} (27) = \frac{3}{2}

ln (x^{2}) = (ln (x))^{2}

lo g_{10} (c) = 10

lo g_{10} (2 x) = 4