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

hartnn
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0understood the property

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

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

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

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

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

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

hartnn
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.020 log 5 means 20 log base 5?

hartnn
 one year 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
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0okay so there is only 1 value for x?

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

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