What is the answer to log_{x}(8)=-2 ?

The answer to log_{x}(8)=-2 is x= 1/(2sqrt(2))

Solve for x: log_{x}(8)=-2

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

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lo g_{x} (8) = - 2

x = \frac{1}{2 2}

Decimal Notation

x = 0.35355 \dots

Solution steps

lo g_{x} (8) = - 2

Apply log rules

\frac{1}{lo g _{8} ( x )} = - 2

Multiply both sides by

lo g_{8} (x)

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

Simplify

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

Switch sides

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

Divide both sides by

- 2

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

Apply log rules

x = \frac{1}{2 2}

Verify Solutions:

x = \frac{1}{2 2}

True

The solution is

x = \frac{1}{2 2}

lo g_{10} (x) + lo g_{10} (30) = 4

lo g_{10} (x) + lo g_{10} (x + 5) = 3

lo g_{10} (x) + lo g_{10} (x + 5) = 1

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

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

What is the answer to log_{x}(8)=-2 ?
The answer to log_{x}(8)=-2 is x= 1/(2sqrt(2))
Solve for x: log_{x}(8)=-2
The solution is x= 1/(2sqrt(2))