What is the answer to log_{3}(x+6)-log_{3}(x-6)=2 ?

The answer to log_{3}(x+6)-log_{3}(x-6)=2 is x= 15/2

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log_{3}(x+6)-log_{3}(x-6)=2

lo g_{3} (x + 6) - lo g_{3} (x - 6) = 2

x = \frac{15}{2}

Decimal Notation

x = 7.5

Solution steps

lo g_{3} (x + 6) - lo g_{3} (x - 6) = 2

Add

lo g_{3} (x - 6)

to both sides

lo g_{3} (x + 6) - lo g_{3} (x - 6) + lo g_{3} (x - 6) = 2 + lo g_{3} (x - 6)

Simplify

lo g_{3} (x + 6) = 2 + lo g_{3} (x - 6)

Apply log rules

x + 6 = 9 (x - 6)

Solve

x + 6 = 9 (x - 6) : x = \frac{15}{2}

x = \frac{15}{2}

Verify Solutions:

x = \frac{15}{2}

True

The solution is

x = \frac{15}{2}

lo g_{10} (2 x - 6) = lo g_{10} (6 - x)

ln (x^{3} + 19) = 3 ln (x + 1)

- 2 lo g_{5} (2 b + 7) = 9

lo g_{4} (5 x - 6) = 4

2 lo g_{2} (x - 1) - lo g_{2} (4 - x) = 2

What is the answer to log_{3}(x+6)-log_{3}(x-6)=2 ?
The answer to log_{3}(x+6)-log_{3}(x-6)=2 is x= 15/2
Solve for x: log_{3}(x+6)-log_{3}(x-6)=2
The solution is x= 15/2