What is the answer to log_{5}(5x+3)-log_{5}(3-x)=1 ?

The answer to log_{5}(5x+3)-log_{5}(3-x)=1 is x= 6/5

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log_{5}(5x+3)-log_{5}(3-x)=1

lo g_{5} (5 x + 3) - lo g_{5} (3 - x) = 1

x = \frac{6}{5}

Decimal Notation

x = 1.2

Solution steps

lo g_{5} (5 x + 3) - lo g_{5} (3 - x) = 1

Add

lo g_{5} (3 - x)

to both sides

lo g_{5} (5 x + 3) - lo g_{5} (3 - x) + lo g_{5} (3 - x) = 1 + lo g_{5} (3 - x)

Simplify

lo g_{5} (5 x + 3) = 1 + lo g_{5} (3 - x)

Apply log rules

5 x + 3 = 5 (3 - x)

Solve

5 x + 3 = 5 (3 - x) : x = \frac{6}{5}

x = \frac{6}{5}

Verify Solutions:

x = \frac{6}{5}

True

The solution is

x = \frac{6}{5}

lo g_{x} (3) = 3 lo g_{3} (9) x

lo g_{10} (3^{3 x + 1}) = 9^{x}

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

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

ln (x - 3) = ln (7 x - 23) - ln (x + 1)

What is the answer to log_{5}(5x+3)-log_{5}(3-x)=1 ?
The answer to log_{5}(5x+3)-log_{5}(3-x)=1 is x= 6/5
Solve for x: log_{5}(5x+3)-log_{5}(3-x)=1
The solution is x= 6/5