What is the answer to log_{x}(4/25)=-2 ?

The answer to log_{x}(4/25)=-2 is x= 1/(e^{\frac{ln(4/25)){2}}}

Solve for x: log_{x}(4/25)=-2

The solution is x= 1/(e^{\frac{ln(4/25)){2}}}

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lo g_{x} (\frac{4}{25}) = - 2

x = \frac{1}{e ^{\frac{l n ( \frac{4}{25} )}{2}}}

Decimal Notation

x = 2.5

Solution steps

lo g_{x} (\frac{4}{25}) = - 2

Apply log rules

\frac{ln ( \frac{4}{25} )}{ln ( x )} = - 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{4}{25} )}{ln ( x )} ln (x) = - 2 ln (x)

Simplify

ln (\frac{4}{25}) = - 2 ln (x)

Switch sides

- 2 ln (x) = ln (\frac{4}{25})

Divide both sides by

- 2

ln (x) = - \frac{ln ( \frac{4}{25} )}{2}

Apply log rules

x = \frac{1}{e ^{\frac{l n ( \frac{4}{25} )}{2}}}

Verify Solutions:

x = \frac{1}{e ^{\frac{l n ( \frac{4}{25} )}{2}}}

True

The solution is

x = \frac{1}{e ^{\frac{l n ( \frac{4}{25} )}{2}}}

ln (x) + ln (x + 1) = ln (20)

lo g_{x} (49) = - 2

ln (3 x - 1) = 2

y, lo g_{e} (y) = a z

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

What is the answer to log_{x}(4/25)=-2 ?
The answer to log_{x}(4/25)=-2 is x= 1/(e^{\frac{ln(4/25)){2}}}
Solve for x: log_{x}(4/25)=-2
The solution is x= 1/(e^{\frac{ln(4/25)){2}}}