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

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

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

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

x = 3

Solution steps

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

Apply log rules

x^{2} = (2 x - 3) \cdot 3

Solve

x^{2} = (2 x - 3) \cdot 3 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

ln (x) + ln (x - 3) = ln (7 x)

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

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

lo g_{10} (3 x) + lo g_{10} (5) = 1

11 = - lo g_{10} (x)

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