What is the answer to log_{3}(x+15)-log_{3}(x-1)=2 ?

The answer to log_{3}(x+15)-log_{3}(x-1)=2 is x=3

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log_{3}(x+15)-log_{3}(x-1)=2

lo g_{3} (x + 15) - lo g_{3} (x - 1) = 2

x = 3

Solution steps

lo g_{3} (x + 15) - lo g_{3} (x - 1) = 2

Add

lo g_{3} (x - 1)

to both sides

lo g_{3} (x + 15) - lo g_{3} (x - 1) + lo g_{3} (x - 1) = 2 + lo g_{3} (x - 1)

Simplify

lo g_{3} (x + 15) = 2 + lo g_{3} (x - 1)

Apply log rules

x + 15 = 9 (x - 1)

Solve

x + 15 = 9 (x - 1) : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

ln (x) = 5.1

ln (x) = 5.6

2 lo g_{10} (x) 8 - lo g_{10} (x) 4 = 2

ln (14 x + 8) = 7

ln (3 x - 14) = 7

What is the answer to log_{3}(x+15)-log_{3}(x-1)=2 ?
The answer to log_{3}(x+15)-log_{3}(x-1)=2 is x=3
Solve for x: log_{3}(x+15)-log_{3}(x-1)=2
The solution is x=3