Solve: logx + log(x + 15) = 2?

Question

It's log of x plus log times x plus 15 equals 2. help please? How do you solve this?

Lavinia Carroll · Accepted Answer

You need to use the logarithm identity,log(A*B) = log(A) + log(B)so,logx + log(x+15) = 2log(x*(x+15)) = 2log (x^2 + 15x) = 2I am assuming you mean log base 10. In that case, we have:x^2 + 15x = 10^2x^2 + 15x = 100x^2 + 15x - 100 = 0Factoring,(x + 20)(x - 5) = 0So, x = -20 or x = 5.

Lavinia Carroll · Answer

log A + log B = log (A • B)logx + log(x + 15) = 2log (x • (x + 15) ) = 2log (x² + 15x) = 210² = x² + 15x100 = x² + 15xx² + 15x - 100 = 0(x + 20) (x - 5) = 0x = -20 and x = 5Plugging them both into the equation you will find that only x = 5 will work since you can't take the log of a negative number so x = -20 is an extraneous solution. The only answer is x = 5.

Lavinia Carroll · Answer

logx + log(x + 15) = 2log(x^2+15x) = 2100 = x^2 + 15xx^2 + 15x - 100 = 0x^2 + 20x - 5x - 100 = 0x(x+20) - 5(x+20) = 0(x-5)(x+20) = 0x = 5 or -20x = 5

Lavinia Carroll · Answer

For the best answers, search on this site https://shorturl.im/EJofRthis is the same as writing: log(x(x-15)) = 2 log(x^2 - 15) = 2 if the base for log is not written then you assume that it is to the base 10 therefore 10^2 = x^2 - 15 100 + 15 = x^2 x^2 = 115 therefore x = sqareroot(115) type that into your calculator and that should give you the answer 🙂 good luck!

Lavinia Carroll · Answer

us your log rules to combine the logs so it becomes log x squared +15x =2 then use the inverser so its 10 squared=x squared+ 15x and factor and if you cant factor use quadratic formula but just a hint you can factor it 🙂

Alize Kuhn

Solve: logx + log(x + 15) = 2?

5 Answers

AI-Powered Insights

Want to answer this question?

Categories

Tags

Related Questions