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Statement1:log10x<logπx<logex<log2x  x>1
Statement2:x<ylogax>logay when 0<a<1
  1. Statement1 is true, Statement2 is true, Statement2 is not a correct explanation of Statement1.
  2. Statement1 is true, Statement2 is false.
  3. Statement1 is false, Statement2 is true.
  4. Statement1 is true, Statement2 is true, Statement2 is a correct explanation of Statement1.


Solution

The correct option is A Statement1 is true, Statement2 is true, Statement2 is not a correct explanation of Statement1.
If base>1, then log function is strictly increasing.
So, when x>1, we have 
logx10>logxπ>logxe>logx2
1logx10<1logxπ<1logxe<1logx2
log10x<logπx<logex<log2x

For 0<a<1, logax is strictly decreasing function of x.
x<ylogax>logay

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