justme
  • justme
log (x-9) + log x = 1
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
radar
  • radar
\[10^{x-9}+10^{x}=10^{0}\] x-9+x=0 2x=9 x=4.5 check:\[10^{4.5-9}+10^{4.5}=10^{0}=1\]
justme
  • justme
wow thanks! the way you wrote it made it so much easier to understand ( :
amistre64
  • amistre64
log(x^2 - 9x) = 1 x^2 - 9x = 10^1 = 10 x^2 - 9x - 10 = 0 (x-10)(x+1) = 0 x = 10, -1 ...... log(10-9) + log(10) = 1 ?? log(1) + 1 = 1 log(1) = 0 10^0 = 1 ... did i do that right?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amistre64
  • amistre64
log(-1-9) = log(-10)...-1 aint an option tho :)
amistre64
  • amistre64
log(4.5 - 9) + log(4.5) = 1 log(-4.5) + log(4.5) logs cant be negative....
amistre64
  • amistre64
bases dont add if they aint got the same exponents x^2 + x^3 doesnt equal x^5
radar
  • radar
Can not you let them be negative to solve this problem?? lol
amistre64
  • amistre64
well; we will have to write the board of logaritms and enter a plea, then the senate will ahve to vote on it .... its just alot of work for one litle problem :)
justme
  • justme
base is 10 because it is not given. so all the bases here are the same.
amistre64
  • amistre64
doesnt matter; bases dont add without like exponents x^2 + x^5 DOESNT EQUAL x^7
amistre64
  • amistre64
10^a + 10^b DOESNT EQUAL 10^(a+b)
amistre64
  • amistre64
logs arent numbers; so they dont work like numbers; they are exponents and follow the rules of exponents
radar
  • radar
Yes, I do see the flaw in such an elegant solution, sorry about that justme, please ignore.
justme
  • justme
so x=4.5 right? seems to work when checked.
amistre64
  • amistre64
log(x-9) + log(x) = 1; exponents add when bases multiply log((x)(x-9)) = 1 log(x^2 -9x) = 1 10^log... = 10^1 x^2 -9x = 10 x^2 -9x -10 = 0 x= 10, -1 ; -1 is illegal to use in the equation becasue log(-1-9) doesnt exist
radar
  • radar
adding as I did was really multiplying, and of course 10^x*10^-x would equal 1.
amistre64
  • amistre64
4.5 is illegal to use; becasue log(-4.9) does not exist
amistre64
  • amistre64
you can tell by graphing the log function and going over to -10 and -4.5 and looking around to find a y value.... it aint there :)
radar
  • radar
You have convinced me this problem is above my pay grade, please post the correct solution if you can or anyone can solve it.
amistre64
  • amistre64
the correct solution is: x = 10. And we all get lost in the math eventually ;)
justme
  • justme
how did you get that?
amistre64
  • amistre64
........ if you scroll up and read the post, i actually typed it out a few times lol
radar
  • radar
wouldn't that result in 11=1 we know thats not right.
amistre64
  • amistre64
log(10-9) + log(10) = 1 log(1) + 1 = 1 log(1) = 0 10^log(1) = 10^0 1 = 10^0 1 = 1
amistre64
  • amistre64
also known as: 0 + 1 = 1
radar
  • radar
Thanks
radar
  • radar
It will work.
radar
  • radar
Justme, did you see the flaw in the way I worked it? I hope I didn't mess you up. But the addition was illegal, as we were dealing with exponents, adding is exponents is the same as multiplying, and your problem was addition. I learned a lot on that thing!!!
justme
  • justme
radar, me too that was the best lesson on log I have seen. thanks!

Looking for something else?

Not the answer you are looking for? Search for more explanations.