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

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

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

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

x = 1, x = 4

Solution steps

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

Apply log rules

lo g_{4} (x) (x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

lo g_{4} (x) = 0 or x - 4 = 0

Solve

lo g_{4} (x) = 0 : x = 1

Solve

x - 4 = 0 : x = 4

Verify Solutions:

x = 1

True

, x = 4

True

The solutions are

x = 1, x = 4

lo g_{10} (c) = 0

lo g_{3} (x + 2) + lo g_{3} (x + 1) = lo g_{3} (x^{2} + 1)

lo g_{22} (2 x) - 5 lo g_{2} (x) = 0

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

ln (8 - 2 x) = \frac{1}{2} ln (4 - x)

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