What is the answer to ln(2x)=2+ln(x-1) ?

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

Solve for x: ln(2x)=2+ln(x-1)

The solution is x=(e^2)/(e^2-2)

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

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

Decimal

x = 1.37112 \dots

Solution steps

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

Apply log rules

2 x = e^{2} (x - 1)

Solve

2 x = e^{2} (x - 1) : x = \frac{e ^{2}}{e ^{2} - 2}

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

Verify Solutions:

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

True

The solution is

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

lo g_{7} (x - 5) + 5 = 7

12 x ln (x) + 6 x = 0

6 + lo g_{8} (- 2 x) = 5

lo g_{x} (2) = 8

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

What is the answer to ln(2x)=2+ln(x-1) ?
The answer to ln(2x)=2+ln(x-1) is x=(e^2)/(e^2-2)
Solve for x: ln(2x)=2+ln(x-1)
The solution is x=(e^2)/(e^2-2)