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

The answer to ln(x-4)=2-ln(x+4) is x=sqrt(e^2+16)

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

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

x = e^{2} + 16

Decimal Notation

x = 4.83622 \dots

Solution steps

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

Add

ln (x + 4)

to both sides

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

Simplify

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

Apply log rules

(x - 4) (x + 4) = e^{2}

Solve

(x - 4) (x + 4) = e^{2} : x = e^{2} + 16, x = - e^{2} + 16

x = e^{2} + 16, x = - e^{2} + 16

Verify Solutions:

x = e^{2} + 16

True

, x = - e^{2} + 16

False

The solution is

x = e^{2} + 16

5 lo g_{7} (x) = lo g_{7} (x^{n})

lo g_{10} (x) = 1.7959

ln (x) = ln (x - 2000) + 1.4

lo g_{4} (8) + lo g_{4} (x) = 5

2 lo g_{4} (x) - lo g_{4} (3 x - 5) = 1

What is the answer to ln(x-4)=2-ln(x+4) ?
The answer to ln(x-4)=2-ln(x+4) is x=sqrt(e^2+16)
Solve for x: ln(x-4)=2-ln(x+4)
The solution is x=sqrt(e^2+16)