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

The answer to log_{3}(x)-log_{3}(2x-1)=2 is x= 9/17

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

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

x = \frac{9}{17}

Decimal Notation

x = 0.52941 \dots

Solution steps

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

Add

lo g_{3} (2 x - 1)

to both sides

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

Simplify

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

Apply log rules

x = 9 (2 x - 1)

Solve

x = 9 (2 x - 1) : x = \frac{9}{17}

x = \frac{9}{17}

Verify Solutions:

x = \frac{9}{17}

True

The solution is

x = \frac{9}{17}

lo g_{3} (x) - lo g_{3} (2 x - 1) = 0

5 ln (3 x) - 2 ln (2 x) = 6

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

0 = ln (1 + (1 + c^{1}))

lo g_{2} (x - 2) + lo g_{2} (2 x - 1) = 0

What is the answer to log_{3}(x)-log_{3}(2x-1)=2 ?
The answer to log_{3}(x)-log_{3}(2x-1)=2 is x= 9/17
Solve for x: log_{3}(x)-log_{3}(2x-1)=2
The solution is x= 9/17