## Vague 2 years ago Log question, let me write it out so it makes more sense!

1. Vague

\[f(x)=\log _{4}(x+2) AND g(x)=\log_{4}(2x-5), please find f(x)=g(x)\]

2. hartnn

use the fact that if log A =logB then A =B can you find an equation in 'x' using that ?

3. mathstudent55

If log a = log b then a = b

4. Joseph91

f(x)=g(x) implies x+2=2x-5 x=7

5. hartnn

for any base, (base of 4 doesn't matter here)

6. Vague

Well, the answer is {7}, (log4(9))

7. Vague

I honestly have no idea how to solve that out, it's review and I can't find it in my notes.

8. harsimran_hs4

for any log expressions with same base to be equal e.g log a = log b be it any base a = b for you just have to simply work out a linear equation

9. hartnn

can you clearly post your question ? a screenshot will be wonderful....

10. Vague

Solve the problem. 1 2 ) f(x) = log4(x + 2) and g(x) = log4( 2 x - 5) . Solve f(x) = g(x). 1 2 ) A) {7} , (7, log4(7) ) B) {7} , (7, log4(9) ) C) {7} , (7, log4(2) ) D) No solution. A n s w e r : B

11. Vague

It's the best I can do, sorry. And when you solve it as a linear equation, would you change it to exponencial form, or can you not do that?

12. harsimran_hs4

you can change but that wouldn`t do any good...... a = e ^ (ln a) (basic property of log)

13. hartnn

ok, did you get how x=7 ? now just put x=7 in any one of f(x) or g(x)

14. Vague

I didn't get x=7, our teacher gave us the answers and I don't know how she got any of them. I'd really like to see someone solve the equation so I can see what you guys are talking about. ;P I tried doing it and got -7/2

15. hartnn

if log A =logB then A =B \(f(x)=g(x) \implies \log_4 (x+2)=\log_4(2x-5) \\ \implies x+2 = 2x-5\) can you solve this linear equation ????

16. Vague

Yeah, it makes x=7. So to get the log4(9), you just put it into one of the equations?

17. hartnn

correct, put in any one of f(x) or g(x)

18. hartnn

19. Vague

Thank you! (:

20. hartnn

welcome ^_^