SOLUTION: Given that P>1 and {{{1/log(2,P)}}} + {{{1/log(3,P)}}} + {{{1/log(5,P)}}} + {{{1/log(7,P)}}} + {{{1/log(11,P)}}} = {{{1/log(x,P)}}}, find the integral value of x

Algebra.Com
Question 1204649: Given that P>1 and + + + + = , find the integral value of x
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Change of base formula

the reciprocal of that is

This idea is used in the 2nd step shown below.



Use the idea mentioned earlier



Use the log rule log(A)+log(B) = log(A*B)







Answer by ikleyn(52767)   (Show Source): You can put this solution on YOUR website!
.
Given that P>1 and + + + + = , find the integral value of x
~~~~~~~~~~~~~~~~~~~~~ 

Use an identity

     = ,

which is valid for any positive real "a" and "b".


Then your equation will take the form

     +  +  +  +  = .


It is the same as

     = ,


which you can transform further

     = 

    x = 2310.


ANSWER.  x = 2310.

Solved.




RELATED QUESTIONS

log(p+q)=log p-log q... (answered by tommyt3rd)
Solve the equation. Log(4p+1) + log(p) =... (answered by AlgebraLady88)
If log (p+q) = log p- log q, show that... (answered by rapaljer)
From the formula A=P(1 + r)x P represents amount of money invested r represents rate... (answered by MathLover1)
If log(p+q)=log p + log q, then show that q=p(q-1) (answered by solver91311)
Given log 2=p log 7=q Find (14^3x+1)(8^2x+3)=7 in terms of p and... (answered by ikleyn)
Write as a single logarithm a) 2 log 5 log b b) 3 log x + 1/2 log y c) 2 log m + log n (answered by lwsshak3)
if log 2=p and log 3=q express the following logarithms in terms of p and q 1. log b... (answered by Tatiana_Stebko,lwsshak3)
1..Given that Log=2Logx +3Log,express p in terms of x and q. (answered by ikleyn)