Question

If 2^x = 10 and 10^y = 128, find x*y.

Answer 1

Step-by-step explanation:

${2}^{x} = 10 \\ takig \: log \: both \: sides \\ \\ log( {2}^{x} ) = log(10) \\ = > x log(2) = log(10) \: \: \\ = > x = \frac{ log(10) }{ log(2) } ........(1)\\ \\ and \\ {10}^{y} = 128 \\ log( {10}^{y} ) = log(128) \\ = > y log(10) = log( {2}^{7} ) \\ = > y log(10) = 7 log(2) \\ = > y = \frac{7 log(2) }{ log(10) } ...........(2) \\ \\ multiplying \: equation \: (1) \: \: and \: \: (2) \\ \\ x \times y = \frac{ log(10) }{ log(2) } \times \frac{7 log(2) }{ log(10) } \\ = > x \times y = 7 \: \: \: ans.$