What is the answer to log_{x}(32/243)=5 ?

The answer to log_{x}(32/243)=5 is x=e^{(ln(32/243))/5}

Solve for x: log_{x}(32/243)=5

The solution is x=e^{(ln(32/243))/5}

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lo g_{x} (\frac{32}{243}) = 5

x = e^{\frac{l n ( \frac{32}{243} )}{5}}

Decimal Notation

x = 0.66666 \dots

Solution steps

lo g_{x} (\frac{32}{243}) = 5

Apply log rules

\frac{ln ( \frac{32}{243} )}{ln ( x )} = 5

Multiply both sides by

ln (x)

\frac{ln ( \frac{32}{243} )}{ln ( x )} ln (x) = 5 ln (x)

Simplify

ln (\frac{32}{243}) = 5 ln (x)

Switch sides

5 ln (x) = ln (\frac{32}{243})

Divide both sides by

5

ln (x) = \frac{ln ( \frac{32}{243} )}{5}

Apply log rules

x = e^{\frac{l n ( \frac{32}{243} )}{5}}

Verify Solutions:

x = e^{\frac{l n ( \frac{32}{243} )}{5}}

True

The solution is

x = e^{\frac{l n ( \frac{32}{243} )}{5}}

0.65 = ln (x)

2 lo g_{10} (x + 6) = lo g_{10} (x + 7)

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

lo g_{10} (x) = 7.2

lo g_{2 x - 1} (3 x^{2} + 6) = 2

What is the answer to log_{x}(32/243)=5 ?
The answer to log_{x}(32/243)=5 is x=e^{(ln(32/243))/5}
Solve for x: log_{x}(32/243)=5
The solution is x=e^{(ln(32/243))/5}