0

solve the question


1/3log3M + 3log3N = 1 + log0.0085

then 

which one is true 
1) M9=9/N
2) N9=9/M
3) M3=3/N
4) N9=3/M


10-Oct-2015 12:52 PM
~12

Answers (1)


0

1st let us find the value of log0.00085.

Let log0.00085 = y.
So 5 = (0.008)y.
5 = (8/1000)y
5 = (2/10)3y
5 = (1/5)3y
5 = (5)-3y
-3y = 1. y = -1/3.
So,  1 + log0.00085  = 1 – 1/3 = 2/3.

Now, the options need us to find a relation between M & N, and hence it should be true for all values of M & N.

We have the equation :1/3 log3M + 3 log3N = 2/3.

Since it is true for all values of M and N,
Let us split and give:

1/3 log3M = 1/3

3 log3N = 1/3.

(as this also satisfies the equation)


That means log3M = 1, and M = 3.
Also, it means, log3N = 1/9.  N = 3(1/9).
N= 3 and M = 3.
So M * N= 3*3 = 9.
This is correct as per the 2nd option.



10-10-2015 21:57
~44

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