What is the answer to log_{x-3}(x-1)=2 ?

The answer to log_{x-3}(x-1)=2 is x=5

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log_{x-3}(x-1)=2

lo g_{x - 3} (x - 1) = 2

x = 5

Solution steps

lo g_{x - 3} (x - 1) = 2

Apply log rules

\frac{ln ( x - 1 )}{ln ( x - 3 )} = 2

Multiply both sides by

ln (x - 3)

\frac{ln ( x - 1 )}{ln ( x - 3 )} ln (x - 3) = 2 ln (x - 3)

Simplify

ln (x - 1) = 2 ln (x - 3)

Apply log rules

x - 1 = (x - 3)^{2}

Solve

x - 1 = (x - 3)^{2} : x = 5, x = 2

x = 5, x = 2

Verify Solutions:

x = 5

True

, x = 2

False

The solution is

x = 5

lo g_{x} (2500) = 2

lo g_{4} (5 x + 9) = 3

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

lo g_{2} (5 x - 1) = 3

ln (x) + ln (x + 10) = 3