Limits of Logarithms
Read this topicExplanations 2
- Logarithms in the form lognx=y\log_n x = ylognx=y means that nnn raised to the power yyy is equal to xxx. The question logny=?\log_n y = ?logny=? asks "to what number should…
By Qinzhuo Zhang, Joshua Siktar, Matt Superdock, Moor Xu
- Logarithms!Logarithms!Logarithms! LogarithmsLogarithmsLogarithms are pretty cool; they were used by the ancients to turn pesky long multiplication and division problems into som…
By Evan Tong
Problems 7
- Evaluate limx→03ln(5x+1)5x\lim_{x\to0}{\frac{3\ln(5x+1)}{5x}}x→0lim5x3ln(5x+1)
- Evaluate limx→04ln(9x+1)3ln(4x+1)\lim_{x\to0}{\frac{4\ln(9x+1)}{3\ln(4x+1)}}x→0lim3ln(4x+1)4ln(9x+1)
- Evaluate limx→14ln(x)7(x−1)\lim_{x\to1}{\frac{4\ln(x)}{7(x-1)}}x→1lim7(x−1)4ln(x)
- Evaluate limx→06ln(1+x7)5ln(1+3x7)\lim_{x\to0}{\frac{6\ln(1+x^7)}{5\ln(1+3x^7)}}x→0lim5ln(1+3x7)6ln(1+x7)
- Evaluate limx→0ln(1+6sin(5x))2x\lim_{x\to0}{\frac{\ln(1+6\sin(5x))}{2x}}x→0lim2xln(1+6sin(5x))
- Evaluate limx→0+xlnx2\lim_{x\to0^+}{\frac{\sqrt{x}\ln{x}}2}x→0+lim2xlnx
- Evaluate limx→0+sin(x)lnx\lim_{x\to0^+}{\sin(x)\ln{x}}x→0+limsin(x)lnx