What is the answer to ln(x^2-5x-1)-ln(3-2x)=0 ?

The answer to ln(x^2-5x-1)-ln(3-2x)=0 is x=-1

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ln(x^2-5x-1)-ln(3-2x)=0

ln (x^{2} - 5 x - 1) - ln (3 - 2 x) = 0

x = - 1

Solution steps

ln (x^{2} - 5 x - 1) - ln (3 - 2 x) = 0

Add

ln (3 - 2 x)

to both sides

ln (x^{2} - 5 x - 1) - ln (3 - 2 x) + ln (3 - 2 x) = 0 + ln (3 - 2 x)

Simplify

ln (x^{2} - 5 x - 1) = ln (3 - 2 x)

Apply log rules

x^{2} - 5 x - 1 = 3 - 2 x

Solve

x^{2} - 5 x - 1 = 3 - 2 x : x = 4, x = - 1

x = 4, x = - 1

Verify Solutions:

x = 4

False

, x = - 1

True

The solution is

x = - 1

ln (\frac{x}{x ^{2} + 1}) = 1

lo g_{2} (x) + 3 lo g_{10} (x) + 2 = 0

ln (x + 4) + ln (x - 2) = 2 ln (x)

lo g_{10} (x) = \frac{1}{x}

lo g_{2} (x) - 2 lo g_{x} (3) = 0

What is the answer to ln(x^2-5x-1)-ln(3-2x)=0 ?
The answer to ln(x^2-5x-1)-ln(3-2x)=0 is x=-1
Solve for x: ln(x^2-5x-1)-ln(3-2x)=0
The solution is x=-1