Question

Integration of \[e^x\]
Given:
\[\large \log_{e}2=0.6931\] and
\[\large \log_{e}3=1.0986\]
, calculate \[\large \log_{10}2\] and \[\large \log_{10}3\]
Verify your results from tables.

Answer 1

Integration?

Answer 2

That's the title/topic on the sheet. This is one of the questions under that title.

Answer 3

And therefore it must have something to do with that.

Answer 4

\[\Large
\log_{10}2 = \frac{\log_e 2}{\log_e 10}
\]

Answer 5

They didn't give you \(\large \log_e 5\)?

Answer 6

Nope. And how did you get that expression?

Answer 7

\[\begin{array}{r}
x &=& \log_{10} 2 \\
10^x &=& 2\\
\log_e10^x&=&\log_e2 \\
x \log_e10&=&\log_e2\\
x &=& \frac{\log_e2}{\log_e10}
\end{array}
\]

Answer 8

Ah yep I see. Thanks for your help. I think I can do the other one now.