What is the answer to ln(x^2-10)-ln(x)=2ln(3) ?

The answer to ln(x^2-10)-ln(x)=2ln(3) is x=10

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ln(x^2-10)-ln(x)=2ln(3)

ln (x^{2} - 10) - ln (x) = 2 ln (3)

x = 10

Solution steps

ln (x^{2} - 10) - ln (x) = 2 ln (3)

Add

ln (x)

to both sides

ln (x^{2} - 10) - ln (x) + ln (x) = 2 ln (3) + ln (x)

Simplify

ln (x^{2} - 10) = 2 ln (3) + ln (x)

Apply log rules

x^{2} - 10 = 9 x

Solve

x^{2} - 10 = 9 x : x = 10, x = - 1

x = 10, x = - 1

Verify Solutions:

x = 10

True

, x = - 1

False

The solution is

x = 10

ln (4 x) = 1

ln (9 - x^{2}) = 0

x, ln (3 x) = 4 y

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

lo g_{x} (9) = \frac{1}{3}

What is the answer to ln(x^2-10)-ln(x)=2ln(3) ?
The answer to ln(x^2-10)-ln(x)=2ln(3) is x=10
Solve for x: ln(x^2-10)-ln(x)=2ln(3)
The solution is x=10