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

The answer to log_{3}(x+2)-log_{3}(x)=2 is x= 1/4

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

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

x = \frac{1}{4}

Solution steps

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

Add

lo g_{3} (x)

to both sides

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

Simplify

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

Apply log rules

x + 2 = 9 x

Solve

x + 2 = 9 x : x = \frac{1}{4}

x = \frac{1}{4}

Verify Solutions:

x = \frac{1}{4}

True

The solution is

x = \frac{1}{4}

lo g_{x} (6) = \frac{1}{3}

ln (3 x - 15) = 5

ln (3 x - 15) = 3

3 ln (8 x - 10) + 15 = 6

lo g_{3} (x + 7) + lo g_{3} (x + 8) = 8

What is the answer to log_{3}(x+2)-log_{3}(x)=2 ?
The answer to log_{3}(x+2)-log_{3}(x)=2 is x= 1/4
Solve for x: log_{3}(x+2)-log_{3}(x)=2
The solution is x= 1/4