Question

if 3(log 5 - log 3) - (log 5 - 2 log 6)= 2 - log x,find x
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Answer 1

Answer:

Given :

3(log5−log3)−(log5−2log6)=2−logn

Let us simplify the given expression to find n,

3log5−3log3−log5+2log6=2−logn

2log5−3log3+2log6=2(1)−logn

log5

2

−log3

3

+log6

2

=2log10−logn[Since,1=log10]

logn=−log25+log27−log36+log100

=(log100+log27)−log5+log36)

=log(100×27)−log(25×36)

=log(100×27)−log(25×36)

=log(100×27)/(25×36)

logn=log3

n=3

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Answer 2

Answer:

Given, 3(log5 - log3) - ( log5 - 2log6 ) = 2 -logx

We know that log a - log b = log a/b ---------- (1)

      3 log 5/3 - log 5/6^2 + logx = 2

      3 log 5/3 - log 5/36 + log x = 2

      We know that a log(x) = log(x)^a

      log (5/3)^3 - log 5/36 + log x = 2

 

      log 125/27 - log 5/36 + log x = log 100

     We know that log(a) - log(b) = log(a/b)

      log 125 * 36 /5 * 27 + log x = log 100

      log 100/3  + log x = log 100

     We  know that log(a + b) = log(ab)

      log 100x/3 = log 100

      x = 100 * 3/100

         = 3.

     x = 3.

Hope this helps!    

Step-by-step explanation: