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

The answer to log_{3}(2x)-log_{3}(x-1)=2 is x= 9/7

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

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

x = \frac{9}{7}

Solution steps

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

Add

lo g_{3} (x - 1)

to both sides

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

Simplify

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

Apply log rules

2 x = 9 (x - 1)

Solve

2 x = 9 (x - 1) : x = \frac{9}{7}

x = \frac{9}{7}

Verify Solutions:

x = \frac{9}{7}

True

The solution is

x = \frac{9}{7}

ln (x + 7) + ln (x - 5) = 2 ln (x)

lo g_{6} (x) = lo g_{3} (4 x)

ln (x + 10) + ln (x - 2) = 2 ln (x)

3 = lo g_{4} (x)

lo g_{2} (y) + lo g_{2} (y + 1) = 1

What is the answer to log_{3}(2x)-log_{3}(x-1)=2 ?
The answer to log_{3}(2x)-log_{3}(x-1)=2 is x= 9/7
Solve for x: log_{3}(2x)-log_{3}(x-1)=2
The solution is x= 9/7