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

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

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

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

x = 2

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Apply log rules

x^{2} - 2 = x

Solve

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

x = 2, x = - 1

Verify Solutions:

x = 2

True

, x = - 1

False

The solution is

x = 2

lo g_{8} (5 x + 47) = 3

y, lo g_{8} (x y) = 3

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

3 = lo g_{b} (125)

lo g_{\frac{1}{8}} (13 - x) = - 2