## Sgstudent 2 years ago 3 log base 5 y - 1og base 25 y = 10 This is a difficult question for me to solve and i hope you would help me thanks.

1. Sgstudent

I know that log base 25 is actually 1/2 log base 5 y

2. hartnn

sure, first you need to know this property of log, \[\log_ba= \dfrac{\log a}{\log b}\]

3. Sgstudent

understood the property

4. hartnn

so, \(\log_5 y= ...?? \\ \log_{25}y=... ?\)

5. Sgstudent

log base 5 y = log y / log 5 and log base 25 y = log y/ log 25

6. hartnn

good :) now \(\log x^n=n \log x \\ so, \log 25=.... ?\)

7. Sgstudent

2 log 5 sir

8. hartnn

so, now you can put log y =x and the equation will become ...?

9. Sgstudent

i dont know

10. Sgstudent

can you give me the full step solution lol

11. Sgstudent

i am getting confuse here

12. hartnn

\(3x/log 5 -x/(2log 5) = 10 \\ \) got this step first ?

13. hartnn

where x=log y

14. Sgstudent

keep it going

15. hartnn

multiply both sides by 2log 5 6x - x = 20 log 5 5x = 20 log 5 got this much ?

16. Sgstudent

The first step that you posted is that the first step of showing the workings?

17. hartnn

if you understand how to solve, you will be able to show the workings on your own....

18. Sgstudent

20 log 5 means 20 log base 5?

19. hartnn

i have made the base unspecified (when its unspecified, by default its 10), so 20 log 5 means 20 times log of 5 (with the base 10)

20. Sgstudent

i dont get it

21. Sgstudent

i think that is where the problem lies in. if not, i could easily understand your workings.

22. hartnn

\(\log_ba= \dfrac{\log_{10} a}{\log_{10} b} \\\log _{25}y =\dfrac{\log_{10} y}{\log_{10} 25} \) now ?

23. Sgstudent

yes

24. hartnn

\(\log_ba= \dfrac{\log_{10} a}{\log_{10} b} \\\log _{25}y =\dfrac{\log_{10} y}{\log_{10} 25}=\dfrac{\log_{10} y}{2\log_{10} 5}\\\log_{5}y=\dfrac{\log_{10} y}{\log_{10} 5} \\ let \log y=x \\ 3x/\log 5 -x/(2\log 5)=10 \implies 6x-x=20\log_{10}5\\x=4\log_{10}5 \\ \log_{10} y = \log _{10}5^4 \implies y= 5^4\)

25. Sgstudent

okay so there is only 1 value for x?

26. hartnn

yes, and so 1 value of y.

27. Sgstudent

so what is it?

28. Sgstudent

i want to see whether i got the right answer.