What is the answer to log_{2}(1/(x^2))=3 ?

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

Solve for x: log_{2}(1/(x^2))=3

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

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lo g_{2} (\frac{1}{x ^{2}}) = 3

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

Decimal Notation

x = 0.35355 \dots, x = - 0.35355 \dots

Solution steps

lo g_{2} (\frac{1}{x ^{2}}) = 3

Apply log rules

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

Multiply both sides by

x^{2}

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

Simplify

1 = 8 x^{2}

Solve

1 = 8 x^{2} : x = \frac{1}{2 2}, x = - \frac{1}{2 2}

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

Verify Solutions:

x = \frac{1}{2 2}

True

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

True

The solutions are

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

5.5 = 6 + lo g_{10} (x)

lo g_{2} (x - 3) + lo g_{2} (2 x - 1) = 0

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

4 + ln (x + 2) = 2

4.8 = lo g_{10} (\frac{x}{1450})

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