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Sgstudent
 3 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.
Sgstudent
 3 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.

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Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0I know that log base 25 is actually 1/2 log base 5 y

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1sure, first you need to know this property of log, \[\log_ba= \dfrac{\log a}{\log b}\]

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0understood the property

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1so, \(\log_5 y= ...?? \\ \log_{25}y=... ?\)

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0log base 5 y = log y / log 5 and log base 25 y = log y/ log 25

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1good :) now \(\log x^n=n \log x \\ so, \log 25=.... ?\)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1so, now you can put log y =x and the equation will become ...?

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0can you give me the full step solution lol

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0i am getting confuse here

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1\(3x/log 5 x/(2log 5) = 10 \\ \) got this step first ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1multiply both sides by 2log 5 6x  x = 20 log 5 5x = 20 log 5 got this much ?

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0The first step that you posted is that the first step of showing the workings?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1if you understand how to solve, you will be able to show the workings on your own....

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.020 log 5 means 20 log base 5?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1i 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)

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0i think that is where the problem lies in. if not, i could easily understand your workings.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1\(\log_ba= \dfrac{\log_{10} a}{\log_{10} b} \\\log _{25}y =\dfrac{\log_{10} y}{\log_{10} 25} \) now ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1\(\log_ba= \dfrac{\log_{10} a}{\log_{10} b} \\\log _{25}y =\dfrac{\log_{10} y}{\log_{10} 25}=\dfrac{\log_{10} y}{2\log_{10} 5}\\\log_{5}y=\dfrac{\log_{10} y}{\log_{10} 5} \\ let \log y=x \\ 3x/\log 5 x/(2\log 5)=10 \implies 6xx=20\log_{10}5\\x=4\log_{10}5 \\ \log_{10} y = \log _{10}5^4 \implies y= 5^4\)

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0okay so there is only 1 value for x?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1yes, and so 1 value of y.

Sgstudent
 3 years ago
Best ResponseYou've already chosen the best response.0i want to see whether i got the right answer.
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