expand the following logarithmic {(4(x-5)^2/x^4(x-1)^3)}

Question

i need help to expand the following logarithm  {(4(x-5)^2/x^4(x-1)^3)}

 

Answer 1

Given log{(4(x-5)^2/x^4(x-1)^3)}

Use the log rules

log(ab) = loga+logb

log(a/b) = loga-logb

logx^a = alogx

log{(4(x-5)^2/x^4(x-1)^3)}

= log4(x-5)^2-logx^4(x-1)^3

= log4+log(x-5)^2-logx^4-log(x-1)^3

= log4+2log(x-5)-4logx-3log(x-1)