But It's Really A Number?

Algebra Level 2

Compute the numerical value of ln ( e x 2 4 ) + ln ( x x ) \displaystyle \ln\left (\sqrt[4]{ex^2} \right )+ \ln\left ( \frac{\sqrt{x}}{x} \right ) .


The answer is 0.25.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Zach Abueg
Jun 30, 2017

ln ( e x 2 4 ) + ln ( x 2 x ) = 1 4 ln ( e x 2 ) + 1 2 ln x ln x = 1 4 ( ln e + 2 ln x ) 1 2 ln x = 1 4 + 1 2 ln x 1 2 ln x = 1 4 \displaystyle \begin{aligned} \ln\left(\sqrt[{\color{#D61F06}{4}}]{ex^2}\right) + \ln\left(\frac{\sqrt[{\color{#3D99F6}{2}}]{x}}{x}\right) & = {\color{#D61F06}{\frac 14}} \ln\left(ex{\color{#20A900}{^2}}\right) + {\color{#3D99F6}{\frac 12}} \ln x - \ln x \\ & = \frac 14 \left(\ln e + {\color{#20A900}{2}}\ln x\right) - \frac 12 \ln x \\ & = \frac 14 + \frac 12 \ln x - \frac 12 \ln x \\ & = \boxed{\displaystyle \frac 14} \end{aligned}

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...