What is the answer to log_{x}(sqrt(3)-1)=-1 ?

The answer to log_{x}(sqrt(3)-1)=-1 is x=(sqrt(3)+1)/2

Solve for x: log_{x}(sqrt(3)-1)=-1

The solution is x=(sqrt(3)+1)/2

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lo g_{x} (3 - 1) = - 1

x = \frac{3 + 1}{2}

Decimal Notation

x = 1.36602 \dots

Solution steps

lo g_{x} (3 - 1) = - 1

Apply log rules

\frac{ln ( 3 - 1 )}{ln ( x )} = - 1

Multiply both sides by

ln (x)

\frac{ln ( 3 - 1 )}{ln ( x )} ln (x) = - 1 \cdot ln (x)

Simplify

ln (3 - 1) = - ln (x)

Move

ln (x)

to the left side

ln (3 - 1) + ln (x) = 0

Move

ln (3 - 1)

to the right side

ln (x) = - ln (3 - 1)

Apply log rules

x = \frac{3}{2} + \frac{1}{2}

Solve

x = \frac{3}{2} + \frac{1}{2} : x = \frac{3 + 1}{2}

x = \frac{3 + 1}{2}

Verify Solutions:

x = \frac{3 + 1}{2}

True

The solution is

x = \frac{3 + 1}{2}

lo g_{3} (6 x + 34) = lo g_{3} (- 2)

lo g_{10} (4 x) + 13 = 14

lo g_{2} (lo g_{5} (x)) = 3

lo g_{n} (\frac{1}{8}) = - 3

ln (x + 2) = 14

What is the answer to log_{x}(sqrt(3)-1)=-1 ?
The answer to log_{x}(sqrt(3)-1)=-1 is x=(sqrt(3)+1)/2
Solve for x: log_{x}(sqrt(3)-1)=-1
The solution is x=(sqrt(3)+1)/2