What is the answer to log_{2x-1}(3.5x^2-2.5x)=2 ?

The answer to log_{2x-1}(3.5x^2-2.5x)=2 is x=2

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log_{2x-1}(3.5x^2-2.5x)=2

lo g_{2 x - 1} (3.5 x^{2} - 2.5 x) = 2

x = 2

Solution steps

lo g_{2 x - 1} (3.5 x^{2} - 2.5 x) = 2

Apply log rules

\frac{ln ( 3.5 x ^{2} - 2.5 x )}{ln ( 2 x - 1 )} = 2

Multiply both sides by

ln (2 x - 1)

\frac{ln ( 3.5 x ^{2} - 2.5 x )}{ln ( 2 x - 1 )} ln (2 x - 1) = 2 ln (2 x - 1)

Simplify

ln (3.5 x^{2} - 2.5 x) = 2 ln (2 x - 1)

Apply log rules

3.5 x^{2} - 2.5 x = (2 x - 1)^{2}

Solve

3.5 x^{2} - 2.5 x = (2 x - 1)^{2} : x = 2, x = 1

x = 2, x = 1

Verify Solutions:

x = 2

True

, x = 1

False

The solution is

x = 2

2 lo g_{b} (5) = lo g_{b} (x)

lo g_{3} (x) = lo g_{x} (9)

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

ln (x) = \frac{6907756}{1000000}

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

What is the answer to log_{2x-1}(3.5x^2-2.5x)=2 ?
The answer to log_{2x-1}(3.5x^2-2.5x)=2 is x=2
Solve for x: log_{2x-1}(3.5x^2-2.5x)=2
The solution is x=2