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

The answer to ln(3)+ln(2x+5)=2ln(x+2) is x=1+2sqrt(3)

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

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

x = 1 + 23

Decimal Notation

x = 4.46410 \dots

Solution steps

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

Apply log rules

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

Solve

3 (2 x + 5) = (x + 2)^{2} : x = 1 + 23, x = 1 - 23

x = 1 + 23, x = 1 - 23

Verify Solutions:

x = 1 + 23

True

, x = 1 - 23

False

The solution is

x = 1 + 23

lo g_{20} (x) = 1 + lo g_{20} (10)

2 lo g_{10} (x + 5) - lo g_{3} (9) = 2

ln (5 x + 4) = 3

ln (5 x + 4) = 0

lo g_{0.5} (x) = 2

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