What is the answer to 2/(log_{5)(x)}=-4 ?

The answer to 2/(log_{5)(x)}=-4 is x= 1/(sqrt(5))

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2/(log_{5)(x)}=-4

\frac{2}{lo g _{5} ( x )} = - 4

x = \frac{1}{5}

Decimal

x = 0.4472135955

Solution steps

\frac{2}{lo g _{5} ( x )} = - 4

Rewrite the equation with

lo g_{5} (x) = u

\frac{2}{u} = - 4

Solve

\frac{2}{u} = - 4 : u = - \frac{1}{2}

u = - \frac{1}{2}

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

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

x = \frac{1}{5}

Verify Solutions:

x = \frac{1}{5}

True

The solution is

x = \frac{1}{5}

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

3 + lo g_{10} (2 x + 5) = 2

lo g_{a} (125) = 3

lo g_{3} (x + 3) = 4

0 = ln (x^{2} - 16)

What is the answer to 2/(log_{5)(x)}=-4 ?
The answer to 2/(log_{5)(x)}=-4 is x= 1/(sqrt(5))
Solve for x: 2/(log_{5)(x)}=-4
The solution is x= 1/(sqrt(5))