What is the answer to log_{x}(27/64)=-3 ?

The answer to log_{x}(27/64)=-3 is x= 1/(e^{\frac{ln(27/64)){3}}}

Solve for x: log_{x}(27/64)=-3

The solution is x= 1/(e^{\frac{ln(27/64)){3}}}

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lo g_{x} (\frac{27}{64}) = - 3

x = \frac{1}{e ^{\frac{l n ( \frac{27}{64} )}{3}}}

Decimal Notation

x = 1.33333 \dots

Solution steps

lo g_{x} (\frac{27}{64}) = - 3

Apply log rules

\frac{ln ( \frac{27}{64} )}{ln ( x )} = - 3

Multiply both sides by

ln (x)

\frac{ln ( \frac{27}{64} )}{ln ( x )} ln (x) = - 3 ln (x)

Simplify

ln (\frac{27}{64}) = - 3 ln (x)

Switch sides

- 3 ln (x) = ln (\frac{27}{64})

Divide both sides by

- 3

ln (x) = - \frac{ln ( \frac{27}{64} )}{3}

Apply log rules

x = \frac{1}{e ^{\frac{l n ( \frac{27}{64} )}{3}}}

Verify Solutions:

x = \frac{1}{e ^{\frac{l n ( \frac{27}{64} )}{3}}}

True

The solution is

x = \frac{1}{e ^{\frac{l n ( \frac{27}{64} )}{3}}}

3 = 4 \cdot lo g_{10} (5 x + 2)

751043 = 48484 \cdot ln (x) + 67854

lo g_{6} (4 x + 8) - 2 = 0

0.1 = lo g_{e} (\frac{x}{100})

ln (x) - ln (x + 2) = 2

What is the answer to log_{x}(27/64)=-3 ?
The answer to log_{x}(27/64)=-3 is x= 1/(e^{\frac{ln(27/64)){3}}}
Solve for x: log_{x}(27/64)=-3
The solution is x= 1/(e^{\frac{ln(27/64)){3}}}