Can someone help me solve this natural log problem?

ln10+ln5x^2=ln8

Question

Can someone help me solve this natural log problem?

ln10+ln5x^2=ln8

zepdrix · Answer

$$\Large\bf\sf \ln(10)+\ln(5x^2)=\ln(8)$$We want to start by applying a rule of logs:$$\large\bf\sf \color{#A57F02}{\log(a)+\log(b)\quad=\quad \log(a\cdot b)}$$

anonymous · Answer

so ln10+ln5x^2=ln(10*5x^2) ??

zepdrix · Answer

Ok good. Let's multiply the 10 and 5,$$\Large\bf\sf \ln(50x^2)=\ln(8)$$

zepdrix · Answer

Apply the inverse of the log function to get rid of the logs on each side.
Or just recognize that both sides are the `same log`, so their contents must be equal.$$\Large\bf\sf 50x^2=8$$

anonymous · Answer

ahhh now thats where I know how to solve, thank you for showing me the steps!! :)

zepdrix · Answer

One thing to be careful of,
Taking the square root of x^2 will give you `two solutions`, plus/minus.

Since we're dealing with logs, you have to careful check and see if both solutions would work. (Meaning make sure you don't end up taking the log of a negative number).

anonymous · Answer

thank you :) i got x = +/- 2.5