What is the answer to (log_{5}(x))^2+5log_{5}(x)+6=0 ?

The answer to (log_{5}(x))^2+5log_{5}(x)+6=0 is x= 1/25 ,x= 1/125

Solve for x: (log_{5}(x))^2+5log_{5}(x)+6=0

The solution is x= 1/25 ,x= 1/125

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(lo g_{5} (x))^{2} + 5 lo g_{5} (x) + 6 = 0

x = \frac{1}{25}, x = \frac{1}{125}

Decimal

x = 0.04, x = 0.008

Solution steps

(lo g_{5} (x))^{2} + 5 lo g_{5} (x) + 6 = 0

Rewrite the equation with

lo g_{5} (x) = u

(u)^{2} + 5 u + 6 = 0

Solve

u^{2} + 5 u + 6 = 0 : u = - 2, u = - 3

u = - 2, u = - 3

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = - 2 : x = \frac{1}{25}

Solve

lo g_{5} (x) = - 3 : x = \frac{1}{125}

x = \frac{1}{25}, x = \frac{1}{125}

Verify Solutions:

x = \frac{1}{25}

True

, x = \frac{1}{125}

True

The solutions are

x = \frac{1}{25}, x = \frac{1}{125}

0.001 = \frac{ln ( x )}{x}

20 x^{3} ln (x) + 9 x^{3} = 0

ln (x) = \frac{1}{3}

56 x^{6} ln (x) + 15 x^{6} = 0

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

What is the answer to (log_{5}(x))^2+5log_{5}(x)+6=0 ?
The answer to (log_{5}(x))^2+5log_{5}(x)+6=0 is x= 1/25 ,x= 1/125
Solve for x: (log_{5}(x))^2+5log_{5}(x)+6=0
The solution is x= 1/25 ,x= 1/125