What is the answer to log_{m}(8/125)=-3 ?

The answer to log_{m}(8/125)=-3 is m= 1/(e^{\frac{ln(8/125)){3}}}

Solve for m: log_{m}(8/125)=-3

The solution is m= 1/(e^{\frac{ln(8/125)){3}}}

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lo g_{m} (\frac{8}{125}) = - 3

m = \frac{1}{e ^{\frac{l n ( \frac{8}{125} )}{3}}}

Decimal Notation

m = 2.5

Solution steps

lo g_{m} (\frac{8}{125}) = - 3

Apply log rules

\frac{ln ( \frac{8}{125} )}{ln ( m )} = - 3

Multiply both sides by

ln (m)

\frac{ln ( \frac{8}{125} )}{ln ( m )} ln (m) = - 3 ln (m)

Simplify

ln (\frac{8}{125}) = - 3 ln (m)

Switch sides

- 3 ln (m) = ln (\frac{8}{125})

Divide both sides by

- 3

ln (m) = - \frac{ln ( \frac{8}{125} )}{3}

Apply log rules

m = \frac{1}{e ^{\frac{l n ( \frac{8}{125} )}{3}}}

Verify Solutions:

m = \frac{1}{e ^{\frac{l n ( \frac{8}{125} )}{3}}}

True

The solution is

m = \frac{1}{e ^{\frac{l n ( \frac{8}{125} )}{3}}}

lo g_{5} (x) = 6

lo g_{5} (x) = 5

0.57 = lo g_{10} (x)

lo g_{x} (4) = - \frac{2}{5}

40 = 10 lo g_{10} (x)

What is the answer to log_{m}(8/125)=-3 ?
The answer to log_{m}(8/125)=-3 is m= 1/(e^{\frac{ln(8/125)){3}}}
Solve for m: log_{m}(8/125)=-3
The solution is m= 1/(e^{\frac{ln(8/125)){3}}}