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

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

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

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

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

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

Decimal Notation

x = 0.75

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

Verify Solutions:

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

True

The solution is

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

x^{2} ln (x) - 4 ln (x) = 0

lo g_{5} (4 x - 7) = lo g_{5} (x + 5)

lo g_{10} (x^{64}) = - 3

lo g_{6} (7 x + 1) = 2

lo g_{5} (10) = lo g_{10} (x)

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