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

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

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

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

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

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

Decimal Notation

q = 1.33333 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (q)

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

Simplify

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

Switch sides

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

Divide both sides by

- 3

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

Apply log rules

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

Verify Solutions:

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

True

The solution is

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

3.4 = lo g_{10} (x)

- lo g_{10} (x) = 6.8

3 lo g_{t} (3) + lo g_{t} (3) = 4

2 ln (5 x) = 4

2 ln (5 x) = 6

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