What is the answer to log_{2x-1}(4.5x)=2 ?

The answer to log_{2x-1}(4.5x)=2 is x=2

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log_{2x-1}(4.5x)=2

lo g_{2 x - 1} (4.5 x) = 2

x = 2

Solution steps

lo g_{2 x - 1} (4.5 x) = 2

Apply log rules

\frac{ln ( 4.5 x )}{ln ( 2 x - 1 )} = 2

Multiply both sides by

ln (2 x - 1)

\frac{ln ( 4.5 x )}{ln ( 2 x - 1 )} ln (2 x - 1) = 2 ln (2 x - 1)

Simplify

ln (4.5 x) = 2 ln (2 x - 1)

Apply log rules

4.5 x = (2 x - 1)^{2}

Solve

4.5 x = (2 x - 1)^{2} : x = 2, x = \frac{1}{8}

x = 2, x = \frac{1}{8}

Verify Solutions:

x = 2

True

, x = \frac{1}{8}

False

The solution is

x = 2

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

ln (ln (x)) = 5

x^{l o g_{3} (x)} = 27 x^{2}

lo g_{8} (2) + lo g_{8} (4 x^{2}) = 1

lo g_{8} (x) = 3

What is the answer to log_{2x-1}(4.5x)=2 ?
The answer to log_{2x-1}(4.5x)=2 is x=2
Solve for x: log_{2x-1}(4.5x)=2
The solution is x=2