What is the answer to log_{4}(x-1)=log_{2}(x-3) ?

The answer to log_{4}(x-1)=log_{2}(x-3) is x=5

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log_{4}(x-1)=log_{2}(x-3)

lo g_{4} (x - 1) = lo g_{2} (x - 3)

x = 5

Solution steps

lo g_{4} (x - 1) = lo g_{2} (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_{5} (x) + lo g_{x} (5) = 2

lo g_{3} (\frac{2 x - 3}{4}) = lo g_{3} (x + 1)

lo g_{10} (x + 2) - lo g_{10} (x + 1) = 1

lo g_{10} (5 x + 2) = 3

ln (x + 3) + ln (x - 1) - 3 = 0

What is the answer to log_{4}(x-1)=log_{2}(x-3) ?
The answer to log_{4}(x-1)=log_{2}(x-3) is x=5
Solve for x: log_{4}(x-1)=log_{2}(x-3)
The solution is x=5