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a and b are positive numbers satisfying 4(log base 10 a)^2+(log base 10 b)^2=1 then find range of a

a and b are positive numbers satisfying 4(log base 10 a)^2+(log base 10 b)^2=1 then find range of a

Grade:11

1 Answers

Vikas TU
14149 Points
6 years ago
4(log base 10 a)^2+(log base 10 b)^2 = 1 can be written as
8 log base 10 a + 4 log base 10 b=1
Hence for the equation to be equal to 1 the extreme conditions are either 8 log base 10 a should be 0 and 4 log base 10 b should be 1
Or
8 log base 10 a should be 1 and 4 log base 10 b should be 0.
Hence by solving a will be in the range 0 to 1.33.

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