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

The answer to log_{3}(2+x)-log_{3}(2-x)=3 is x= 13/7

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

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

x = \frac{13}{7}

Solution steps

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

Add

lo g_{3} (2 - x)

to both sides

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

Simplify

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

Apply log rules

2 + x = 27 (2 - x)

Solve

2 + x = 27 (2 - x) : x = \frac{13}{7}

x = \frac{13}{7}

Verify Solutions:

x = \frac{13}{7}

True

The solution is

x = \frac{13}{7}

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

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

What is the answer to log_{3}(2+x)-log_{3}(2-x)=3 ?
The answer to log_{3}(2+x)-log_{3}(2-x)=3 is x= 13/7
Solve for x: log_{3}(2+x)-log_{3}(2-x)=3
The solution is x= 13/7