What is the answer to 2ln(x-6)=-4 ?

The answer to 2ln(x-6)=-4 is x= 1/(e^2)+6

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2ln(x-6)=-4

2 ln (x - 6) = - 4

x = \frac{1}{e ^{2}} + 6

Decimal Notation

x = 6.13533 \dots

Solution steps

2 ln (x - 6) = - 4

Divide both sides by

2

ln (x - 6) = - 2

Apply log rules

x - 6 = \frac{1}{e ^{2}}

Solve

x - 6 = \frac{1}{e ^{2}} : x = \frac{1}{e ^{2}} + 6

x = \frac{1}{e ^{2}} + 6

Verify Solutions:

x = \frac{1}{e ^{2}} + 6

True

The solution is

x = \frac{1}{e ^{2}} + 6

ln (x - 5) + ln (5 x + 1) = 10

lo g_{4} (x + 1) + lo g_{4} (x - 1) = 4

lo g_{5} (b) = - 3

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

lo g_{2} (39 x) - lo g_{2} (x - 5) = 4