which set represents the complete list of solutions of the equation log(10x)+log(x-3)=2? How do u do this?

Question

asnaseer · Answer

do you know your log rules?
e.g. log(a) + log(b) = log(ab)

anonymous · Answer

Yes

asnaseer · Answer

so use that rule to first simplify the left-hand-side of the equation.

anonymous · Answer

so you get 10x^2-30x=2. Do you subtract the 2 to the left side and then use the quadratic formula?

asnaseer · Answer

not quite, what you get first is:
log(10x^2-30x)=2

asnaseer · Answer

is the log function here base 10 or is it the natural log?

anonymous · Answer

What do you mean by natural log?

asnaseer · Answer

natural log of x would be $log_e(x)$
base 10 log of x would be $log_{10}(x)$

asnaseer · Answer

right, so next you need to use the definition of what a log is, i.e.:$$\text{if }\quad log_{10}(x)=y$$then$$x=10^y$$

asnaseer · Answer

can you see what to do next?

anonymous · Answer

10^(10x^2-30x)=2 ?

asnaseer · Answer

no - try again - look carefully at the definition of what a log represents

anonymous · Answer

Ohh sorry it's 100=10x^2-30x

asnaseer · Answer

perfect! - so now you just need to solve this quadratic equation and you are home and dry!

anonymous · Answer

Thank you for taking your time to help!:)

asnaseer · Answer

no problem - you're welcome