What is the answer to log_{e}(x-2)-3log_{e}(2)=2 ?

The answer to log_{e}(x-2)-3log_{e}(2)=2 is x=8e^2+2

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log_{e}(x-2)-3log_{e}(2)=2

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

x = 8 e^{2} + 2

Decimal Notation

x = 61.11244 \dots

Solution steps

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

Move

3 lo g_{e} (2)

to the right side

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

Apply log rules

x - 2 = 8 e^{2}

Solve

x - 2 = 8 e^{2} : x = 8 e^{2} + 2

x = 8 e^{2} + 2

Verify Solutions:

x = 8 e^{2} + 2

True

The solution is

x = 8 e^{2} + 2

ln (x + 5) - ln (x - 4) = ln (x)

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

ln (x) + ln (x + 1) = 2

1.85 = - lo g_{10} (x)

lo g_{x} (0.1) = - \frac{1}{3}

What is the answer to log_{e}(x-2)-3log_{e}(2)=2 ?
The answer to log_{e}(x-2)-3log_{e}(2)=2 is x=8e^2+2