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Mathematics 13 Online
OpenStudy (jiteshmeghwal9):

Plz help:)

jhonyy9 (jhonyy9):

can you rewrite it using paranthesis ?

OpenStudy (apoorvk):

okay let me provide a hint: \[\log_ab^n = n\log_ab\] Can you apply this to the very first term?

OpenStudy (jiteshmeghwal9):

Sorry, for misunderstanding all of u.My ques. is:-\[\log_{5}{(5^{1/x}+125)} =\log_{5}{6+1+(1/2)x} \]

OpenStudy (jiteshmeghwal9):

@apoorvk Plz help:)

OpenStudy (apoorvk):

\(1 = \log_55\) and \(x/2= \log_55^{x/2}\) Replace it and then club the logs together. And then solve!

OpenStudy (jiteshmeghwal9):

can u give me full solution plz.

OpenStudy (apoorvk):

Do you know the properties of logarithms?

OpenStudy (jiteshmeghwal9):

Ya!

OpenStudy (jiteshmeghwal9):

are u there @apoorvk ?

OpenStudy (apoorvk):

okay, what's --> \(\log_56+\log_55 + \log_55^{x/2}=??\)

OpenStudy (jiteshmeghwal9):

I couldn't understood wht u wants to say:(

OpenStudy (jiteshmeghwal9):

Is anybody here????

OpenStudy (jiteshmeghwal9):

Plz help. I need helppppppppppp.

OpenStudy (apoorvk):

do you know that \(\log_ma+\log_mb+....+\log_mn=\log_m(a\times b\times....\times n)\)??

OpenStudy (jiteshmeghwal9):

ya!

OpenStudy (apoorvk):

so can you apply that to the expression I wrote above and find out its equivalent?

OpenStudy (jiteshmeghwal9):

I gt \[\log_{5}{30\times5{x/2}} \]

OpenStudy (jiteshmeghwal9):

@apoorvk

OpenStudy (apoorvk):

that would be actually \(\log_5(30\times 5^{x/2})\) that's what you meant right?

OpenStudy (jiteshmeghwal9):

Ya!

OpenStudy (apoorvk):

Hmm, so now this term equals the LHS, that is \(\log_5(5^{1/x}+ 125)\). Now since the bases are same, you can take antilog and remove the log signs, so that the arguments equal each other. (Btw, are you sure that the '125' is a part of the argument of the log in the LHS?)

OpenStudy (jiteshmeghwal9):

Ya!i m totally sure that 125 is a part of the argument of the log in the LHS.

OpenStudy (jiteshmeghwal9):

The answer given in my book is 1/2 or 1/4.

OpenStudy (jiteshmeghwal9):

One minute I think at R.H.S.the argument of log is only to 6.

OpenStudy (apoorvk):

so, \(5^{1/x}+125 = 30\times 5^{x/2}\)

OpenStudy (apoorvk):

WHAT?? I REQUEST you to please read it correctly yaar, ye toh paagal ho gaya main :O :p

OpenStudy (jiteshmeghwal9):

Nooooo ! I m only thinking about this becoz at R.H.S. there is no bracket like those at L.H.S.

OpenStudy (jiteshmeghwal9):

Do u understand??????

OpenStudy (jiteshmeghwal9):

I have written the correct ques.

OpenStudy (jiteshmeghwal9):

Itna sannata kyun hai????

OpenStudy (experimentx):

http://www.wolframalpha.com/input/?i=Solve [Log[30*5^%28x%2F2%29]+%3D%3D+Log[125+%2B+5^%281%2Fx%29]%2C+x]

OpenStudy (jiteshmeghwal9):

so wht is ur conclusion @experimentX

OpenStudy (experimentx):

must be some kind of typo in question.

OpenStudy (jiteshmeghwal9):

K! I gt it .i also thought that there is some type of typo. Thanx!

OpenStudy (experimentx):

if the answer is 1/2 and 1/4 then there must be some typo. try solving by pluggin to wolfram.

OpenStudy (jiteshmeghwal9):

K!

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