What is the answer to log_{x}(5)=-2 ?

The answer to log_{x}(5)=-2 is x= 1/(sqrt(5))

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log_{x}(5)=-2

lo g_{x} (5) = - 2

x = \frac{1}{5}

Decimal

x = 0.4472135955

Solution steps

lo g_{x} (5) = - 2

Apply log rules

\frac{1}{lo g _{5} ( x )} = - 2

Multiply both sides by

lo g_{5} (x)

\frac{1}{lo g _{5} ( x )} lo g_{5} (x) = - 2 lo g_{5} (x)

Simplify

1 = - 2 lo g_{5} (x)

Switch sides

- 2 lo g_{5} (x) = 1

Divide both sides by

- 2

lo g_{5} (x) = - \frac{1}{2}

Apply log rules

x = \frac{1}{5}

Verify Solutions:

x = \frac{1}{5}

True

The solution is

x = \frac{1}{5}

y, x = 2 y + ln (y)

lo g_{7} (x + 2) = - 2

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

lo g_{3} (x - 2) = 4

lo g_{9} (x) = 0.5

What is the answer to log_{x}(5)=-2 ?
The answer to log_{x}(5)=-2 is x= 1/(sqrt(5))
Solve for x: log_{x}(5)=-2
The solution is x= 1/(sqrt(5))