I am taking a math class online in which I need to solve Algebra problems by hand without a calculator. I am getting caught up on how to solve log by hand. Whats a simple way to solve log(1.66)? we have to test via webcam with a piece of paper, and no calculator. Any advice?
[Math] Solving Log(1.66) without a calculator.
logarithms
Best Answer
For logs you are basically in for Taylor series methods, supplemented by whatever values you have available in tables or memorized. You also have a tradeoff between how accurate you want to be and how much work you are willing to do. You didn't say what the base of the logs is. If it is base $10$, I know $\log_{10} 2\approx 0.30103$ and $\log_{10} 3 \approx 0.477$, so I would say $\log_{10} 1.66 \approx \log_{10} 5 - \log_{10} 3 \approx 1-0.301 - 0.477 = 0.222$. If they are natural logs, I know $\log 2 \approx 0.693$ so would say $\log 1.66 = \log 2 + \log (1-0.16) \approx 0.693 -0.16 + \frac {0.16^2}2-\frac {0.16^3}3$ where the next term is less than $0.001$ so I have three place accuracy. Dividing out the $2$ made the distance from $1$ smaller so the Taylor series converges more quickly.