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

The answer to log_{3}((2x)/(x-1))=2 is x= 9/7

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

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

x = \frac{9}{7}

Decimal Notation

x = 1.28571 \dots

Solution steps

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

Apply log rules

\frac{2 x}{x - 1} = 3^{2}

Multiply both sides by

x - 1

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

Simplify

2 x = 9 (x - 1)

Solve

2 x = 9 (x - 1) : x = \frac{9}{7}

x = \frac{9}{7}

Verify Solutions:

x = \frac{9}{7}

True

The solution is

x = \frac{9}{7}

lo g_{10} (3 x + 6) = lo g_{10} (3) + 1

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

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

lo g_{10} (x) = 0.4104

x = a^{l o g_{a} (x)}

What is the answer to log_{3}((2x)/(x-1))=2 ?
The answer to log_{3}((2x)/(x-1))=2 is x= 9/7
Solve for x: log_{3}((2x)/(x-1))=2
The solution is x= 9/7