Question

Find the value of log9 0.24. (hint: log2=0.301 log3=0.477)

Answer 1

Answer: -0.65 approximately

Work Shown:

`\log_(9)(0.24) = (\log(0.24))/(\log(9))\\\\\log_(9)(0.24) = (\log(0.03*8))/(\log(3^2))\\\\\log_(9)(0.24) = (\log(3*10^(-2)*2^3))/(\log(3^2))\\\\\log_(9)(0.24) = (\log(3)+\log(10^(-2))+\log(2^3))/(\log(3^2))\\\\\log_(9)(0.24) = (\log(3)-2\log(10)+3\log(2))/(2\log(3))\\\\\log_(9)(0.24) \approx (0.477-2*1+3*0.301)/(2*0.477)\\\\\log_(9)(0.24) \approx (-0.62)/(0.954)\\\\\log_(9)(0.24) \approx -0.649895\\\\\log_(9)(0.24) \approx -0.65\\\\`