What is the answer to log_{5}(3x+5)-log_{5}(5-x)=2 ?

The answer to log_{5}(3x+5)-log_{5}(5-x)=2 is x= 30/7

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log_{5}(3x+5)-log_{5}(5-x)=2

lo g_{5} (3 x + 5) - lo g_{5} (5 - x) = 2

x = \frac{30}{7}

Decimal Notation

x = 4.28571 \dots

Solution steps

lo g_{5} (3 x + 5) - lo g_{5} (5 - x) = 2

Add

lo g_{5} (5 - x)

to both sides

lo g_{5} (3 x + 5) - lo g_{5} (5 - x) + lo g_{5} (5 - x) = 2 + lo g_{5} (5 - x)

Simplify

lo g_{5} (3 x + 5) = 2 + lo g_{5} (5 - x)

Apply log rules

3 x + 5 = 25 (5 - x)

Solve

3 x + 5 = 25 (5 - x) : x = \frac{30}{7}

x = \frac{30}{7}

Verify Solutions:

x = \frac{30}{7}

True

The solution is

x = \frac{30}{7}

ln (3 x - 5) - 2 ln (x) = ln (2)

lo g_{3} (- 7 x + 1) - 7 = - 4

lo g_{3} (32) = 5 lo g_{3} (x)

6 lo g_{49} (r) = 3

y, ln (y - 32) = 5 t

What is the answer to log_{5}(3x+5)-log_{5}(5-x)=2 ?
The answer to log_{5}(3x+5)-log_{5}(5-x)=2 is x= 30/7
Solve for x: log_{5}(3x+5)-log_{5}(5-x)=2
The solution is x= 30/7