Solve for x: Logarithmic Equation with Multiple Terms - Step by Step Guide

[nikita33]

Homework Statement

log x² + log x - log 2.7 = log 10
solve for x

Homework Equations

The Attempt at a Solution

this one i really don't know how to do. I can't find any examples, but this is what i tried (youre going to be like, what? but i had to attempt it.) I think when logs are in addition format, youre supposed to multiply them? does that make sense? i really need help on this one. :

2 log x + log x = log 10 + log 2.7
2 log x² = log 27
4 log x = log 27

thats as far as i can get. i know its wrong. even one step in the right direction would help me.

 

[Dick]

No, 2*log(x)+log(x) IS NOT 2*log(x^2). 2*log(x)+log(x)=3*log(x)=log(27). Try it from there. Or do log(x^2)+log(x)=log(x^3)=log(27).

 

[nikita33]

^
i had it that way the first time. i think i changed it because i got

3 log x = log 27
then to solve for x i got something that looks like this:

x = log 27/3 log

3 log? is it supposed to be 3 log 1?

if so, the answer is 0. i put 0 on my exam, although i set it up incorrectly. my prof would give a point for the correct answer and i got no points, so i don't think that's the answer.

 

[Mark44]

"3 log" makes no sense. Go back a step to 3 log x = log 27.

What's another way to write 3 log x?

 

[Dick]

3*log(x)=log(x^3), doesn't it? 3log(x) is not 3*log*x. That's just plain silly, as Mark44 points out.