What is the answer to log_{2}((3x+1)/(2x-7))=3 ?

The answer to log_{2}((3x+1)/(2x-7))=3 is x= 57/13

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log_{2}((3x+1)/(2x-7))=3

lo g_{2} (\frac{3 x + 1}{2 x - 7}) = 3

x = \frac{57}{13}

Decimal Notation

x = 4.38461 \dots

Solution steps

lo g_{2} (\frac{3 x + 1}{2 x - 7}) = 3

Apply log rules

\frac{3 x + 1}{2 x - 7} = 2^{3}

Multiply both sides by

2 x - 7

\frac{3 x + 1}{2 x - 7} (2 x - 7) = 2^{3} (2 x - 7)

Simplify

3 x + 1 = 8 (2 x - 7)

Solve

3 x + 1 = 8 (2 x - 7) : x = \frac{57}{13}

x = \frac{57}{13}

Verify Solutions:

x = \frac{57}{13}

True

The solution is

x = \frac{57}{13}

lo g_{2} (x) = 0.3

10 0^{l o g_{10} (x)} = 2 x^{3}

ln (x) + ln (2 x - 11) = ln (21)

lo g_{16} (x) = lo g_{2} (x)

ln (c x^{9}) = 9 ln (c) + 9 ln (x)

What is the answer to log_{2}((3x+1)/(2x-7))=3 ?
The answer to log_{2}((3x+1)/(2x-7))=3 is x= 57/13
Solve for x: log_{2}((3x+1)/(2x-7))=3
The solution is x= 57/13