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

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

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log_{x}(|x^2-1|)=2

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

x = \frac{1}{2}

Decimal

x = 0.70710 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Apply log rules

x^{2} - 1 = x^{2}

Solve

x^{2} - 1 = x^{2} : x = - \frac{1}{2} or x = \frac{1}{2}

x = - \frac{1}{2} or x = \frac{1}{2}

Verify Solutions:

x = - \frac{1}{2}

False

, x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

y, lo g_{y} (137) = x

lo g_{2} (2 x + 16) = 2

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

5 = ln (x)

ln (x - 2) = 3

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