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

The answer to log_{3}((x+1)/(2x+1))=2 is x=-8/17

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

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

x = - \frac{8}{17}

Decimal Notation

x = - 0.47058 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

2 x + 1

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

Simplify

x + 1 = 9 (2 x + 1)

Solve

x + 1 = 9 (2 x + 1) : x = - \frac{8}{17}

x = - \frac{8}{17}

Verify Solutions:

x = - \frac{8}{17}

True

The solution is

x = - \frac{8}{17}

lo g_{10} (x) = 8

ln (x) = 10.12939661

x, 0.72 = ln (x)

lo g_{5} (x + 7) + lo g_{5} (x + 3) = 1

lo g_{3} (x^{3} + 19) = 3

What is the answer to log_{3}((x+1)/(2x+1))=2 ?
The answer to log_{3}((x+1)/(2x+1))=2 is x=-8/17
Solve for x: log_{3}((x+1)/(2x+1))=2
The solution is x=-8/17