What is the answer to log_{2}((3x+1)/(4x-3))=3 ?

The answer to log_{2}((3x+1)/(4x-3))=3 is x= 25/29

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log_{2}((3x+1)/(4x-3))=3

lo g_{2} (\frac{3 x + 1}{4 x - 3}) = 3

x = \frac{25}{29}

Decimal Notation

x = 0.86206 \dots

Solution steps

lo g_{2} (\frac{3 x + 1}{4 x - 3}) = 3

Apply log rules

\frac{3 x + 1}{4 x - 3} = 2^{3}

Multiply both sides by

4 x - 3

\frac{3 x + 1}{4 x - 3} (4 x - 3) = 2^{3} (4 x - 3)

Simplify

3 x + 1 = 8 (4 x - 3)

Solve

3 x + 1 = 8 (4 x - 3) : x = \frac{25}{29}

x = \frac{25}{29}

Verify Solutions:

x = \frac{25}{29}

True

The solution is

x = \frac{25}{29}

lo g_{x} (6) = \frac{1}{2}

lo g_{2} (2 x + 5) = 3

ln (x) + ln (7 x + 1) = 1

lo g_{5} (n^{2} + 20 n) = 3

lo g_{2} (x - 5) = 2 - lo g_{2} (x - 8)

What is the answer to log_{2}((3x+1)/(4x-3))=3 ?
The answer to log_{2}((3x+1)/(4x-3))=3 is x= 25/29
Solve for x: log_{2}((3x+1)/(4x-3))=3
The solution is x= 25/29