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

The answer to log_{3}((2+x)/(2-x))=3 is x= 13/7

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

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

x = \frac{13}{7}

Decimal

x = 1.85714 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

2 - x

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

Simplify

2 + x = 27 (2 - x)

Solve

2 + x = 27 (2 - x) : x = \frac{13}{7}

x = \frac{13}{7}

Verify Solutions:

x = \frac{13}{7}

True

The solution is

x = \frac{13}{7}

lo g_{10} (5 x - 1) = 2 lo g_{10} (x - 2)

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

lo g_{7} (x^{2} - 3 x + 3) = 0

lo g_{3} (7 x - 15) = 3

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

What is the answer to log_{3}((2+x)/(2-x))=3 ?
The answer to log_{3}((2+x)/(2-x))=3 is x= 13/7
Solve for x: log_{3}((2+x)/(2-x))=3
The solution is x= 13/7