Question

log (x-9) + log x = 1

Answer 1

\[10^{x-9}+10^{x}=10^{0}\]
x-9+x=0
2x=9
x=4.5

check:\[10^{4.5-9}+10^{4.5}=10^{0}=1\]

Answer 2

wow thanks! the way you wrote it made it so much easier to understand ( :

Answer 3

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?

Answer 4

log(-1-9) = log(-10)...-1 aint an option tho :)

Answer 5

log(4.5 - 9) + log(4.5) = 1

log(-4.5) + log(4.5)

logs cant be negative....

Answer 6

bases dont add if they aint got the same exponents

x^2 + x^3 doesnt equal x^5

Answer 7

Can not you let them be negative to solve this problem?? lol

Answer 8

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 :)

Answer 9

base is 10 because it is not given. so all the bases here are the same.

Answer 10

doesnt matter; bases dont add without like exponents

x^2 + x^5 DOESNT EQUAL x^7

Answer 11

10^a + 10^b DOESNT EQUAL 10^(a+b)

Answer 12

logs arent numbers; so they dont work like numbers; they are exponents and follow the rules of exponents

Answer 13

Yes, I do see the flaw in such an elegant solution, sorry about that justme, please ignore.

Answer 14

so x=4.5 right? seems to work when checked.

Answer 15

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

Answer 16

adding as I did was really multiplying, and of course 10^x*10^-x would equal 1.

Answer 17

4.5 is illegal to use; becasue log(-4.9) does not exist

Answer 18

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 :)

Answer 19

You have convinced me this problem is above my pay grade, please post the correct solution if you can or anyone can solve it.

Answer 20

the correct solution is:

x = 10.

And we all get lost in the math eventually ;)

Answer 21

how did you get that?

Answer 22

........ if you scroll up and read the post, i actually typed it out a few times lol

Answer 23

wouldn't that result in 11=1 we know thats not right.

Answer 24

log(10-9) + log(10) = 1

log(1) + 1 = 1

log(1) = 0

10^log(1) = 10^0

1 = 10^0

1 = 1

Answer 25

also known as:

0 + 1 = 1

Answer 26

Thanks

Answer 27

It will work.

Answer 28

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!!!

Answer 29

radar, me too that was the best lesson on log I have seen. thanks!