Question

(log2 49) (log7 2) (1097 7) is equal to:

Answer 1

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ log_{2}(49) \times log_{7}(2) \times log_{7}(7) }$

EVALUATION

$\displaystyle \sf{ log_{2}(49) \times log_{7}(2) \times log_{7}(7) }$

$\displaystyle \sf{ = \frac{ log(49) }{ log(2) } \times \frac{ log(2) }{ log(7) } \times \frac{ log(7) }{ log(7) } }$

$\displaystyle \sf{ = \frac{ log(49) }{ log(7) } \times \frac{ log(7) }{ log(7) } }$

$\displaystyle \sf{ = \frac{ log( {7}^{2} ) }{ log(7) } \times 1}$

$\displaystyle \sf{ = \frac{ 2log( {7}^{} ) }{ log(7) } }$

$\displaystyle \sf{ = 2 }$