What is the answer to log_{3}(x+7)-log_{3}(x-7)=2 ?

The answer to log_{3}(x+7)-log_{3}(x-7)=2 is x= 35/4

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log_{3}(x+7)-log_{3}(x-7)=2

lo g_{3} (x + 7) - lo g_{3} (x - 7) = 2

x = \frac{35}{4}

Decimal Notation

x = 8.75

Solution steps

lo g_{3} (x + 7) - lo g_{3} (x - 7) = 2

Add

lo g_{3} (x - 7)

to both sides

lo g_{3} (x + 7) - lo g_{3} (x - 7) + lo g_{3} (x - 7) = 2 + lo g_{3} (x - 7)

Simplify

lo g_{3} (x + 7) = 2 + lo g_{3} (x - 7)

Apply log rules

x + 7 = 9 (x - 7)

Solve

x + 7 = 9 (x - 7) : x = \frac{35}{4}

x = \frac{35}{4}

Verify Solutions:

x = \frac{35}{4}

True

The solution is

x = \frac{35}{4}

y, x = ln (2 y - 1)

3 lo g_{8} (2 x + 7) + 8 = 10

lo g_{4} (x - 3) + lo g_{4} (4 x + 3) = 1

lo g_{x} (2) = 128

x ln (x) - x = 0

What is the answer to log_{3}(x+7)-log_{3}(x-7)=2 ?
The answer to log_{3}(x+7)-log_{3}(x-7)=2 is x= 35/4
Solve for x: log_{3}(x+7)-log_{3}(x-7)=2
The solution is x= 35/4