Pojęcie logarytmu

Pojęcie logarytmu

\mathrm{\log _{\mathrm{2}}8=}\textcolor{#005FD4}{\mathrm{3}} log2 8  =  3 ,  ponieważ \left.\mleft.2\mright.\right.^{\mleft.\textcolor{#005FD4}{3}\mright.}=8 23  =  8

\mathrm{\log _{\mathrm{5}}1=}\textcolor{#005FD4}{\mathrm{0}} log5 1  =  0 ,  ponieważ \left.\mleft.5\mright.\right.^{\mleft.\textcolor{#005FD4}{0}\mright.}=1 50  =  1

\mathrm{\log _2} log2 \frac{1}{8}=\textcolor{#005FD4}{-3} 18  =  −3 ,  ponieważ\left.\mleft.2\mright.\right.^{\mleft.\textcolor{#005FD4}{-3}\mright.}=\frac{1}{8} 2−3  =  18

\mathrm{\log _{\mathrm{49}}7=} log49 7  =  \frac{\textcolor{#005FD4}{1}}{\textcolor{#005FD4}{2}} 12 ,  ponieważ\left.\mleft.49\mright.\right.^{\mleft.\frac{\textcolor{#005FD4}{1}}{\textcolor{#005FD4}{2}}\mright.}=7 4912  =  7

\mathrm{\log _{}100=}\textcolor{#005FD4}{\mathrm{2}} log 100  =  2 ,  ponieważ \left.\mleft.10\mright.\right.^{\mleft.\textcolor{#005FD4}{2}\mright.}=100 102  =  100

\mathrm{\log _{\mathrm{a}}b=} loga b  = x x ,  gdy \left.\mleft.a\mright.\right.^{\mleft.x\mright.}=\mathit{b} ax  =  b