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

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

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

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

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

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

Decimal Notation

x = 0.66666 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Switch sides

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

Divide both sides by

- 2

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

Apply log rules

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

Verify Solutions:

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

True

The solution is

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

x, y = ln (x - 1)

4 ln (6 x) = - 4

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

3 lo g_{10} (4 - x) = 1 - x

\frac{9}{8} lo g_{2} (x) = - 10

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