What is the answer to log_{x}(4/9)=-2 ?

The answer to log_{x}(4/9)=-2 is x= 1/(e^{\frac{ln(4/9)){2}}}

Solve for x: log_{x}(4/9)=-2

The solution is x= 1/(e^{\frac{ln(4/9)){2}}}

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lo g_{x} (\frac{4}{9}) = - 2

x = \frac{1}{e ^{\frac{l n ( \frac{4}{9} )}{2}}}

Decimal

x = 1.5

Solution steps

lo g_{x} (\frac{4}{9}) = - 2

Apply log rules

\frac{ln ( \frac{4}{9} )}{ln ( x )} = - 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{4}{9} )}{ln ( x )} ln (x) = - 2 ln (x)

Simplify

ln (\frac{4}{9}) = - 2 ln (x)

Switch sides

- 2 ln (x) = ln (\frac{4}{9})

Divide both sides by

- 2

ln (x) = - \frac{ln ( \frac{4}{9} )}{2}

Apply log rules

x = \frac{1}{e ^{\frac{l n ( \frac{4}{9} )}{2}}}

Verify Solutions:

x = \frac{1}{e ^{\frac{l n ( \frac{4}{9} )}{2}}}

True

The solution is

x = \frac{1}{e ^{\frac{l n ( \frac{4}{9} )}{2}}}

lo g_{10} (x) - lo g_{10} (x + 2) = 1

lo g_{10} (x + 6) = lo g_{10} (x) + lo g_{10} (6)

5 x + 3 ln (x - 4) = 25

lo g_{2} (\frac{x}{4}) = 1

lo g_{5} (9 - 2 x) = 2

What is the answer to log_{x}(4/9)=-2 ?
The answer to log_{x}(4/9)=-2 is x= 1/(e^{\frac{ln(4/9)){2}}}
Solve for x: log_{x}(4/9)=-2
The solution is x= 1/(e^{\frac{ln(4/9)){2}}}