Property 3
\(\log a=\log_{10}a\)
\(\log100=\log_{10}10^2=2\)
\(\log\samefrac1{10}=\log10^{-1}=-1\)
\(\log0{,}00001=\log10^{-5}=-5\)
\(\ln a=\log_ea\Rightarrow\) (Natural logarithm)
\(e=2{,}718281\ldots\)
\(\ln e=1\)
\(\ln\samefrac1{e^2}=\ln e^{-2}=-2\)
\(\ln e^{-5}=-5\)
\(\ln1=0\)
1.
\(\ln e^2-\log_{25}5=?\)
2.
\(\log100+\log_{216}36=?\)
3.
\(\log_3 3+\log10=?\)
4.
\(\log10+\log_2 8=?\)
5.
\(\ln e^2+\ln\samefrac1e-\ln e^3=?\)
6.
\(\ln e^3-\log_4 64=?\)
Property 4
\(\blacksquare\quad \log_a b+\log_a c=\log_a(b\cdot c)\)
\(\blacksquare\quad \log_a b-\log_a c=\log_a\left(\samefrac bc\right)\)
1.
\(\log2+\log5=?\)
2.
\(\log_6 4+\log_6 9=?\)
3.
\(\log_2 12-\log_2 3=?\)
4.
\(\log_3 15+\log_3 6-\log_3 10=?\)
5.
\(\log2=x\)
\(\log3=y\)
\(\Rightarrow\log12=?\)
6.
\(\log(2x+1)-\log(x+2)=0\)
\(\Rightarrow x=?\)
7.
\(\log3=x\)
\(\log5=y\)
\(\Rightarrow\log150=?\)