Question

Which of the following is equivalent to log816? (Little 8)

A. 2
B. 1.248
C. 4/3
D. 3/4

Answer 1

`\log_ab=c\iff a^c=b\\\\\log_816=x\iff8^x=16\\\\8=2^3;\ 16=2^4\\\\therefore\\\\8^x=16\to(2^3)^x=2^4\\\\2^(3x)=2^4\iff3x=4\ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=(4)/(3)}\to\fbox{C.}`