## Confucious 3 years ago I'm not good with logs, can someone help me? log(x+2)+log(x-1)=1

1. henkjan

log(x+2)+log(x-1) = log ((x+2)(x-1)) maybe that helps ;P

2. henkjan

And perhaps another helpful rule: if log(a)=b than 10^b = a only in the case when 10 is the basenumber of the logaritm, but if it is not stated otherwise it is always 10.

3. henkjan

So (x+2)(x-1) = 10^1 x^2+x-2= 10 x^2+x-12 = 0 Solve for x and find x = -4 and x = 3

4. Confucious

but it's equal to one??, in the first line you have the equation equal to 10

5. henkjan

I applied the rule I explained in my second post here. because b is in this case 1, it means that 10^1 = a a = (x-1)(x+2) in this case

6. Confucious

isn't the b 10?

7. henkjan

no, the b is equal to the right side in this equation log ((x+2)(x-1)) =1 ...... so it's 1

8. Confucious

okay

9. Confucious

so if the equation was equal to 2 the b would be 10^2?

10. henkjan

log(x)+log(y) = log(x*y) if log(a)=b then 10^b = a only 2 rules I used

11. henkjan

yes, indeed than it would be a = 10^2 = 100

12. Confucious

:) alright, the answer at the back of the text is just 3, why isn't the -4 acceptable?

13. henkjan

oh, right.... a logaritmic can never have a negative number log(-x) is not possible... as 10^b = a ... a can only become positive in this formula

14. Confucious

oh okay, thank you very much