Find the value of

Question

log 8 base 3÷( log 16 base 9 ×log 10 base 4)

Options:

1. 3.log 2 base 10

2. 7.log3 base 10

Answer 1

If x=log_bN and y=log_b² N we have

b^x  = (b² )^y=b^2y or that y=x/2 or x=2y  Also log_cx/log_cy=log_yx

Now log₃8÷( log₉16×log₄10 )=log₃8/(2log₃16×log₄10)=log₁₆8/2log₄10=2log₄8/(2log₄10)=log₁₀8=3log₁₀2