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

The answer to log_{3}(x+1)-log_{3}(2-x)=1 is x= 5/4

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

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

x = \frac{5}{4}

Solution steps

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

Add

lo g_{3} (2 - x)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 3 (2 - x)

Solve

x + 1 = 3 (2 - x) : x = \frac{5}{4}

x = \frac{5}{4}

Verify Solutions:

x = \frac{5}{4}

True

The solution is

x = \frac{5}{4}

4 lo g_{9} (x) = 0

lo g_{2} (n) = 3

- lo g_{10} (x) = 4.3

lo g_{3} (4 x) = lo g_{6} (x)

lo g_{3} (x + 7) = lo g_{3} (x - 1) + 2

What is the answer to log_{3}(x+1)-log_{3}(2-x)=1 ?
The answer to log_{3}(x+1)-log_{3}(2-x)=1 is x= 5/4
Solve for x: log_{3}(x+1)-log_{3}(2-x)=1
The solution is x= 5/4