What is the answer to 2ln(x)-ln(2x-3)=ln(5x)-ln(x+2) ?

The answer to 2ln(x)-ln(2x-3)=ln(5x)-ln(x+2) is x=3,x=5

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

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

x = 3, x = 5

Solution steps

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

Add

ln (x + 2)

to both sides

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

Simplify

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

Apply log rules

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

Solve

x^{2} (x + 2) = 5 x (2 x - 3) : x = 0, x = 3, x = 5

x = 0, x = 3, x = 5

Verify Solutions:

x = 0

False

, x = 3

True

, x = 5

True

The solutions are

x = 3, x = 5

2 x ln (x) + x = 0

lo g_{b} (x)

2 lo g_{10} (x - 1) = lo g_{10} (2 x + 2)

lo g_{10} (x - 2) + lo g_{10} (12 - x) = 0

lo g_{x} (25) = 4

What is the answer to 2ln(x)-ln(2x-3)=ln(5x)-ln(x+2) ?
The answer to 2ln(x)-ln(2x-3)=ln(5x)-ln(x+2) is x=3,x=5
Solve for x: 2ln(x)-ln(2x-3)=ln(5x)-ln(x+2)
The solution is x=3,x=5