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

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

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

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

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

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

Decimal Notation

x = 1.5

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Switch sides

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

Divide both sides by

5

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

Apply log rules

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

Verify Solutions:

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

True

The solution is

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

lo g_{7} (x^{2}) = 2 lo g_{7} (x)

ln (- x + 2) = 6

ln (x - 3) + ln (x - 5) = ln (x + 6)

0.36 = ln (x)

1 = - 1 - 5 \cdot ln (x)

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