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

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

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

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

x = \frac{3}{2}

Decimal

x = 1.5

Solution steps

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

Apply log rules

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

Multiply both sides by

x - 1

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

Simplify

2 x + 1 = 8 (x - 1)

Solve

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

x = \frac{3}{2}

Verify Solutions:

x = \frac{3}{2}

True

The solution is

x = \frac{3}{2}

10 lo g_{10} (\frac{x}{2}) = 5

2 \times lo g_{4} (x) = - 4

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

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

lo g_{e} (x) = x

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