What is the answer to log_{4/x}(x^2-6)=2 ?

The answer to log_{4/x}(x^2-6)=2 is x=2sqrt(2)

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log_{4/x}(x^2-6)=2

lo g_{\frac{4}{x}} (x^{2} - 6) = 2

x = 22

Decimal Notation

x = 2.82842 \dots

Solution steps

lo g_{\frac{4}{x}} (x^{2} - 6) = 2

Apply log rules

\frac{ln ( x ^{2} - 6 )}{ln ( \frac{4}{x} )} = 2

Multiply both sides by

ln (\frac{4}{x})

\frac{ln ( x ^{2} - 6 )}{ln ( \frac{4}{x} )} ln (\frac{4}{x}) = 2 ln (\frac{4}{x})

Simplify

ln (x^{2} - 6) = 2 ln (\frac{4}{x})

Apply log rules

x^{2} - 6 = \frac{16}{x ^{2}}

Solve

x^{2} - 6 = \frac{16}{x ^{2}} : x = 22, x = - 22

x = 22, x = - 22

Verify Solutions:

x = 22

True

, x = - 22

False

The solution is

x = 22

3 ln (x + 5) = 2 ln (7 - x)

- \frac{7}{3} ln (2) = ln (b)

lo g_{2.718} (a) = 1277.29

ln (y) = 3 x^{2} + C, y

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

What is the answer to log_{4/x}(x^2-6)=2 ?
The answer to log_{4/x}(x^2-6)=2 is x=2sqrt(2)
Solve for x: log_{4/x}(x^2-6)=2
The solution is x=2sqrt(2)