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

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

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

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

x = \frac{2}{3}

Solution steps

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

Apply log rules

\frac{2 x}{4 x - 2} = 2^{1}

Multiply both sides by

4 x - 2

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

Simplify

2 x = 2 (4 x - 2)

Solve

2 x = 2 (4 x - 2) : x = \frac{2}{3}

x = \frac{2}{3}

Verify Solutions:

x = \frac{2}{3}

True

The solution is

x = \frac{2}{3}

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

lo g_{7} (2 x) + lo g_{7} (2) = 5

2 ln (x - 1) + ln (x + 7) = 3 ln (x)

lo g_{4} (\frac{1}{2} x + 1) = 3.2

lo g_{10} (x) = 5.48

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