What is the answer to ln(x+2)-ln(4x+3)=-ln(x) ?

The answer to ln(x+2)-ln(4x+3)=-ln(x) is x=3

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ln(x+2)-ln(4x+3)=-ln(x)

ln (x + 2) - ln (4 x + 3) = - ln (x)

x = 3

Solution steps

ln (x + 2) - ln (4 x + 3) = - ln (x)

Add

ln (4 x + 3)

to both sides

ln (x + 2) - ln (4 x + 3) + ln (4 x + 3) = - ln (x) + ln (4 x + 3)

Simplify

ln (x + 2) = - ln (x) + ln (4 x + 3)

Add

ln (x)

to both sides

ln (x + 2) + ln (x) = - ln (x) + ln (4 x + 3) + ln (x)

Simplify

ln (x + 2) + ln (x) = ln (4 x + 3)

Apply log rules

(x + 2) x = 4 x + 3

Solve

(x + 2) x = 4 x + 3 : x = 3, x = - 1

x = 3, x = - 1

Verify Solutions:

x = 3

True

, x = - 1

False

The solution is

x = 3

4.6 = - lo g_{10} (x)

ln (x^{2}) + 2 ln (x) = 0

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

ln (10 - 2 x) = 1

lo g_{10} (x) = - 1.2973

What is the answer to ln(x+2)-ln(4x+3)=-ln(x) ?
The answer to ln(x+2)-ln(4x+3)=-ln(x) is x=3
Solve for x: ln(x+2)-ln(4x+3)=-ln(x)
The solution is x=3