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

The answer to log_{3}(x+3)-log_{3}(x-3)=3 is x= 42/13

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

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

x = \frac{42}{13}

Solution steps

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

Add

lo g_{3} (x - 3)

to both sides

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

Simplify

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

Apply log rules

x + 3 = 27 (x - 3)

Solve

x + 3 = 27 (x - 3) : x = \frac{42}{13}

x = \frac{42}{13}

Verify Solutions:

x = \frac{42}{13}

True

The solution is

x = \frac{42}{13}

lo g_{10} (5 x) + lo g_{10} (14) = 1

ln (k) = 2

lo g_{x} (1728) = 3

y, x = ln ∣ y ∣

lo g_{3} (lo g_{8} (x)) = 1

What is the answer to log_{3}(x+3)-log_{3}(x-3)=3 ?
The answer to log_{3}(x+3)-log_{3}(x-3)=3 is x= 42/13
Solve for x: log_{3}(x+3)-log_{3}(x-3)=3
The solution is x= 42/13