Question

log2 base 3 × log 3 base 4 ×...........×log 99 to base 100

Answer 1

Hey!

$log_{3}(2) \times log_{4}(3) \times .......... \times log_{99}(98) \times log_{100}(99) \\ = \frac{log2}{ log(3) } \times \frac{ log(3) }{ log(4) } \times .......... \times \frac{ log(98) }{ log(99) } \times \frac{ log(99) }{ log(100) } \\ = \frac{ log(2) }{ log(100) } \\ = \frac{ log(2) }{ log( {10}^{2} ) } \\ = \frac{1}{2} log_{10}(2) \\ = \frac{1}{2 } \times 0.301 \\ = 0.1505$

Hope helped!