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mathmath333
 one year ago
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mathmath333
 one year ago
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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} \text{find }\ \log_{10}3\ \text{without calculator }\ \hspace{.33em}\\~\\ \end{align}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It really depends on how accurate you'd like it to be... We can use the power series of \(\ln(1+x)\) to make a decent approximation. \[\ln(1+x)=\sum_{n=1}^\infty\frac{(x)^n}{n}=x\frac{x^2}{2}+\frac{x^3}{3}\cdots\] Change the base to the natural one, then use the series above: \[\log_{10}3=\frac{\ln3}{\ln10}=\frac{\ln(1+2)}{\ln(1+9)}\] At least that's how I would approach it if I didn't have the luxury of using a calculator.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i need 2 decimal places

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0how long do need to write the first series for 2 decimal places

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0approximation correct upto 2 decimal places
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