What is the answer to log_{3}(x+3)-log_{3}(x-5)=2 ?

The answer to log_{3}(x+3)-log_{3}(x-5)=2 is x=6

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log_{3}(x+3)-log_{3}(x-5)=2

lo g_{3} (x + 3) - lo g_{3} (x - 5) = 2

x = 6

Solution steps

lo g_{3} (x + 3) - lo g_{3} (x - 5) = 2

Add

lo g_{3} (x - 5)

to both sides

lo g_{3} (x + 3) - lo g_{3} (x - 5) + lo g_{3} (x - 5) = 2 + lo g_{3} (x - 5)

Simplify

lo g_{3} (x + 3) = 2 + lo g_{3} (x - 5)

Apply log rules

x + 3 = 9 (x - 5)

Solve

x + 3 = 9 (x - 5) : x = 6

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

x = e^{\frac{l n ( x )}{x}}

lo g_{x} (x) = 3

ln (3 x) - 1 = 0

5 = 2 lo g_{10} (x)

lo g_{2} (12 - 2^{x}) = 2 x

What is the answer to log_{3}(x+3)-log_{3}(x-5)=2 ?
The answer to log_{3}(x+3)-log_{3}(x-5)=2 is x=6
Solve for x: log_{3}(x+3)-log_{3}(x-5)=2
The solution is x=6