Show that : 2.log(8/45)+3.log(25/8)-4.log(5/6)=log2

Aman Bansal
592 Points
11 years ago

Dear Anurag,

Use the following logarithmic properties

1. logb(xy) = logbx + logby.
2. logb(x/y) = logbx - logby.
3. logb(xn) = n logbx.
4. logbx = logax / logab.

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renu akunuri
37 Points
11 years ago
=2log8-2log45+3log25-3log8-4log5+4log6

=  -log8-2log45+6log5-4log5+2log36

= -log8-2log45+2log 5+2log36

= -log8+2log (5*36)/45

=-log8 +2log 4

= - log8+ log16

= log 16/8

=log 2

Rishav
15 Points
5 years ago
2log8-2log45+3log25-3log8-4log5+4log6
= -log8-2log45+6log5-4log5+4log6
= -log8-2log45+2log5+4log6
= -3log2-2log5-4log3+2log5+4log2+4log3
= log2