[latex]log_ab=ciff a^c=b\\a > 0 wedge a
eq1 wedge b > 0[/latex]
1.
Dziedzina funkcji
[latex]D:xinmathbb{R^+}[/latex]
[latex]a) log_{sqrt3}x=dfrac{1}{2} o x=left(sqrt3
ight)^frac{1}{2}=left(3^frac{1}{2}
ight)^frac{1}{2}=3^{frac{1}{2}cdotfrac{1}{2}}=3^frac{1}{4}=sqrt[4]3\\b) log_frac{1}{2}x=-1 o x=left(dfrac{1}{2}
ight)^{-1}=2\\c) log_2x=-5 o x=2^{-5}=left(dfrac{1}{2}
ight)^5=dfrac{1}{32}\\d) log x=2 o x=10^2=100\\e) log x=sqrt3 o x=10^{sqrt3}\\f) log x=-0,5 o x=10^{-0,5}=left(dfrac{1}{10}
ight)^frac{1}{2}=dfrac{1}{sqrt{10}}=dfrac{sqrt{10}}{10} [/latex]
2.
Dziedzina funkcji
[latex]D:xinmathbb{R^+}-{1}[/latex]
[latex]a) log_x3^9=3 o x^3=3^9 o x^3=3^{3cdot3} o x^3=(3^3)^3 o x=27\\b) log_x7=-dfrac{1}{2} o x^{-frac{1}{2}}=7 o x^frac{1}{2}=dfrac{1}{7} o x=left(dfrac{1}{7}
ight)^2 o x=dfrac{1}{49}\\c) log_x5=-2 o x^{-2}=5 o x^2=dfrac{1}{5} o x=sqrt{dfrac{1}{5}} o x=dfrac{sqrt5}{5}\\d) log_x0,0001=-8 o x^{-8}=0,0001 o x^8=10000\\ o x^8=10^4 o x^8=left(sqrt{10}
ight)^8 o x=sqrt{10}[/latex]
[latex]e) log_x0,5=-dfrac{1}{2} o x^{-frac{1}{2}}=0,5 o x^{-frac{1}{2}}=dfrac{1}{2} o x^frac{1}{2}=2\\ o x=2^2 o x=4[/latex]
