Prove that 1/log(base 2) n + 1/log(base 3) n+ +1/log(base 50) n=1/log (base50!)n - Maths - Logarithms

Question

Prove that 1/log(base 2) n + 1/log(base 3) n+ +1/log(base 50)
n=1/log (base50!)n

Kavita Verma · Accepted Answer

Dear Student,

1log2n+ 1log3n + 1log4n +
+ 1log50n= logn2 + logn3 + logn4 + 
+ logn50  
as logab = 1logba= logn2×3×4×
×50  
as logba + logbc = logbac= logn50! 
here 50! means 50 factorial= 1log50!n 
as logab = 1logbaHence proved

Regards,

Prove that 1/log(base 2) n + 1/log(base 3) n+...+1/log(base 50) n=1/log (base50!)n