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

The answer to log_{3}(x)-log_{3}(x-2)=2 is x= 9/4

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

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

x = \frac{9}{4}

Solution steps

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

Add

lo g_{3} (x - 2)

to both sides

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

Simplify

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

Apply log rules

x = 9 (x - 2)

Solve

x = 9 (x - 2) : x = \frac{9}{4}

x = \frac{9}{4}

Verify Solutions:

x = \frac{9}{4}

True

The solution is

x = \frac{9}{4}

3 ln (5 x) = 15

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

x, 2 ln (x) + 1 = 0

ln (x) = 8.536595743

x = x ln (x)

What is the answer to log_{3}(x)-log_{3}(x-2)=2 ?
The answer to log_{3}(x)-log_{3}(x-2)=2 is x= 9/4
Solve for x: log_{3}(x)-log_{3}(x-2)=2
The solution is x= 9/4