What is the answer to (ln(x+1))/2 =ln(x-5) ?

The answer to (ln(x+1))/2 =ln(x-5) is x=8

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(ln(x+1))/2 =ln(x-5)

\frac{ln ( x + 1 )}{2} = ln (x - 5)

x = 8

Solution steps

\frac{ln ( x + 1 )}{2} = ln (x - 5)

Multiply both sides by

2

\frac{ln ( x + 1 )}{2} \cdot 2 = ln (x - 5) \cdot 2

Simplify

ln (x + 1) = ln (x - 5) \cdot 2

Apply log rules

x + 1 = (x - 5)^{2}

Solve

x + 1 = (x - 5)^{2} : x = 8, x = 3

x = 8, x = 3

Verify Solutions:

x = 8

True

, x = 3

False

The solution is

x = 8

- lo g_{10} (x) = 2

2 lo g_{x} (3) - lo g_{3} (x) + 1 = 0

lo g_{e} (x) = 2

ln (x - 2) + ln (12 - x) = 0

lo g_{8} (x - 5) = \frac{2}{3}

What is the answer to (ln(x+1))/2 =ln(x-5) ?
The answer to (ln(x+1))/2 =ln(x-5) is x=8
Solve for x: (ln(x+1))/2 =ln(x-5)
The solution is x=8