No calculator

Number Theory Level 3

Without using a calculator, find the value of log ⁡ 10 1024 \log _{ 10 }{ 1024 } , given that l n ( 2 ) = 0.69315 ln(2)=0.69315 and l n ( 2.5 ) = 0.91629 ln(2.5)=0.91629


The answer is 3.0103.

Joel Yip by Joel Yip , 21, Singapore

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Formulae used in the following solution

  • log ⁡ a b = log ⁡ c b log ⁡ c a \log_{a}{b} = \frac{\log_{c}{b}}{\log_{c}{a}}

  • log ⁡ a b c = c × log ⁡ a b \log_{a}{b^c}=c \times \log_{a}{b}

  • log ⁡ a ( b × c ) = log ⁡ a b + log ⁡ a c \log_{a}{(b\times c)}=\log_{a}{b}+\log_{a}{c}

log ⁡ 10 1024 = 10 × log ⁡ e 2 log ⁡ e 10 = 10 × log ⁡ e 2 log ⁡ e 2.5 + 2 × log ⁡ e 2 \log_{10}{1024} = 10 \times \frac{\log_{e}{2}}{\log_{e}{10}}=10 \times \frac{\log_{e}{2}}{\log_{e}{2.5 + 2\times \log_{e}{2}}}

Which can be evaluated using given values

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...