## anonymous one year ago Please Help! I will fan and medal. Use the inverse properties of logarithms to simplify the expression. e^(ln 3)

1. jim_thompson5910

Rule: $\LARGE e^{\ln(x)} = x$ $\LARGE \ln\left(e^x\right) = x$

2. anonymous

Is that the simplified equation? @jim_thompson5910

3. jim_thompson5910

you will use one of those two equations to answer the question

4. anonymous

how do i know which one

5. jim_thompson5910

the question is e^(ln(3)) there's only one number in it: 3 so why not replace x with 3

6. jim_thompson5910

and then try to match up the question with one of the equations given above

7. anonymous

Okay so it would be the first equation? @jim_thompson5910

8. jim_thompson5910

that is correct

9. anonymous

So what now

10. jim_thompson5910

replace x with 3

11. anonymous

e^(ln(3))=3 @jim_thompson5910

12. jim_thompson5910

yes

13. jim_thompson5910

the e^x and ln(x) functions are inverses of each other one goes forward, the other takes you in reverse so they undo each other it's like multiplication and division

14. anonymous

alright so now what? @jim_thompson5910

15. jim_thompson5910

you're done. The answer is 3

16. jim_thompson5910

$\LARGE e^{\ln(x)} = x$ $\LARGE e^{\ln(3)} = 3$

17. jim_thompson5910

$$\LARGE e^{\ln(3)}$$ simplifies to $$\LARGE 3$$

18. anonymous

so the answer is 3 @jim_thompson5910

19. jim_thompson5910

yes

20. anonymous

thank you @jim_thompson5910

21. jim_thompson5910

you're welcome