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Evaluate the limit x tends to zerolog(1+5x) whole divided by x.

\(lim _{xto :0}left(frac{ln left(1+5xright)}{x}right)\)

Apply Lhospital rule,

\(=lim _{xto :0}left(frac{frac{5}{1+5x}}{1}right)\) \(=lim _{xto :0}left(frac{5}{1+5x}right)\)

Plug in the value x=0

\(=frac{5}{1+5cdot :0}\) =5

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