What is the answer to log_{x-1}(x+2)=-1 ?

The answer to log_{x-1}(x+2)=-1 is x=(-1+sqrt(13))/2

Solve for x: log_{x-1}(x+2)=-1

The solution is x=(-1+sqrt(13))/2

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

x = \frac{- 1 + 13}{2}

Decimal Notation

x = 1.30277 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x - 1)

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

Simplify

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

Add

ln (x - 1)

to both sides

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

Simplify

ln (x + 2) + ln (x - 1) = 0

Apply log rules

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

Solve

(x + 2) (x - 1) = 1 : x = \frac{- 1 + 13}{2}, x = \frac{- 1 - 13}{2}

x = \frac{- 1 + 13}{2}, x = \frac{- 1 - 13}{2}

Verify Solutions:

x = \frac{- 1 + 13}{2}

True

, x = \frac{- 1 - 13}{2}

False

The solution is

x = \frac{- 1 + 13}{2}

104 = 20 lo g_{10} (x)

ln (\frac{X}{0.025}) = - 1.18

ln (x^{2} + x) = ln (x^{2}) + ln (x)

lo g_{4} (6 x - 7) = 1

y, ln (9 y) = 2 t + 9

What is the answer to log_{x-1}(x+2)=-1 ?
The answer to log_{x-1}(x+2)=-1 is x=(-1+sqrt(13))/2
Solve for x: log_{x-1}(x+2)=-1
The solution is x=(-1+sqrt(13))/2