## BelleFlower 2 years ago Please wait for image. Logarithms

1. BelleFlower

2. hartnn

which one ?

3. BelleFlower

Q16

4. hartnn

for part (i), take log on both sides, log p=.... ?

5. BelleFlower

lg p = lg a^loga x ?

6. hartnn

yes, now use, $$\log m^n=m \log n$$

7. hartnn

sorry, n log m

8. hartnn

what u get ?

9. BelleFlower

lg p = loga x * lg a

10. hartnn

write log, not lg now use, $$\huge \log_ab=\frac{\log b}{\log a}$$ so what is log_a x = ??

11. BelleFlower

log x / log a

12. hartnn

now substitute that in log p = loga x * log a

13. BelleFlower

I'm not sure what to do but is it: log p = (log x/log a) * log a ?

14. hartnn

really ? just cancel out log a from numerator and denominator.... what remains ??

15. hartnn

and yes, its that

16. hartnn

shall i write out all steps ??

17. BelleFlower

Oh wait I got it ><' Thank you so much! :)

18. hartnn

u want part 2 also ??

19. BelleFlower

Yup

20. hartnn

$$If, x=\log_ab \implies b=a^x$$ so what about , q=log_4 3 ??

21. BelleFlower

3 = 4^x

22. hartnn

u mean 3=4^q ??

23. BelleFlower

sorry yup

24. hartnn

now u need 3^(1/q) =... ? so what will u do ??

25. BelleFlower

I'm not sure..?

26. hartnn

raise both sides to (1/q) exponent...

27. BelleFlower

How do you do that sorry

28. hartnn

$$\huge 3^{(1/q)}= (4^q)^{1/q}$$

29. hartnn

$$\huge (4^q)^{1/q}=.....?$$

30. BelleFlower

4

31. BelleFlower

right?

32. hartnn

yes.

33. hartnn

and you are done ..

34. BelleFlower

okay thanks a lot!

35. hartnn

welcome ^_^