Solution 3.3:3a
From Förberedande kurs i matematik 1
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- | {{ | + | By writing the argument |
- | < | + | <math>\text{8}</math> |
- | {{ | + | as |
+ | <math>8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3}</math>, the logarithm law, | ||
+ | <math>\lg a^{b}=b\lg a</math>, gives | ||
+ | |||
+ | |||
+ | <math>\log _{2}8=\log _{2}2^{3}=3\centerdot \log _{2}2=3\centerdot 1=3</math> | ||
+ | |||
+ | |||
+ | where we have used | ||
+ | <math>\log _{2}2=1</math>. |
Revision as of 13:57, 25 September 2008
By writing the argument \displaystyle \text{8} as \displaystyle 8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3}, the logarithm law, \displaystyle \lg a^{b}=b\lg a, gives
\displaystyle \log _{2}8=\log _{2}2^{3}=3\centerdot \log _{2}2=3\centerdot 1=3
where we have used
\displaystyle \log _{2}2=1.