Question

Solve the following logarithmic equations. ln(32x^2) − 3 ln(2) = 3

Answer 1

Answer:

$x=\pm \frac{\sqrt{e^{3} } }{2}$

Step-by-step explanation:

Rewrite the equation using the next propierties:

$log(\frac{1}{x} )=-log(x)$

$ylog(x)=log(x^{y} )$

$log(x*y)=log(x)+log(y)$

$ln(32x^{2} )-ln(2^{3})=3\\ ln(32x^{2} )+ln(\frac{1}{2^{3} } )=3\\ln(\frac{32x^{2} }{8})=3\\ ln(4x^{2} )=3$

Cancel logarithms by taking exp of both sides:

$e^{ln(4x^{2}) } =e^{3} \\4x^{2} =e^{3}$

Divide both sides by 4:

$x^{2} =\frac{e^{3} }{4}$

Take the square root of both sides:

$x=\pm \sqrt{\frac{e^{3} }{4} } =\pm \frac{\sqrt{e^{3} } }{2}$