Oblicz x: * log[latex]_{x} [/latex] (2x+3)=0 * log[latex]_{x} [/latex] 125=3 * log[latex]_{x} [/latex] [latex] frac{1}{25} [/latex]=-2 * log[latex]_{(2x-5)} [/latex]16=2 *log[latex] sqrt{3-x} [/latex]0,25=-2

[latex]log_{x} (2x+3)=0[/latex] Dziedzina: [latex]x>0,x eq 1[/latex] [latex]2x+3>0 Rightarrow 2x>-3 Rightarrow x>-1,5[/latex] [latex]2x+3=x^0[/latex] [latex]2x+3=1[/latex] [latex]2x=1-3[/latex] [latex]2x=-2 /:2[/latex] [latex]x=-1 otin D[/latex] =========================== [latex]log_{x} 125=3[/latex] Dziedzina: [latex]x>0,x eq 1[/latex] [latex]x^3=125[/latex] [latex]x^3=5^3[/latex] [latex]x=5[/latex] =========================== [latex]log_{x} frac{1}{25} =-2[/latex] Dziedzina: [latex]x>0,x eq 1[/latex] [latex]x^{-2}= frac{1}{25}[/latex] [latex]x^{-2}=5^{-2}[/latex] [latex]x=5[/latex] =========================== [latex]log_{(2x-5)} 16=2[/latex] Dziedzina: [latex]2x-5>0 Rightarrow 2x>5 Rightarrow x>2,5[/latex] [latex]2x-5 eq 1 Rightarrow 2x eq 6 Rightarrow x eq 3[/latex] [latex](2x-5)^2=16[/latex] [latex](2x-5)^2-16=0[/latex] [latex](2x-5-4)(2x-5+4)=0[/latex] [latex](2x-9)(2x-1)=0[/latex] [latex]2x-9=0 lub 2x-1=0[/latex] [latex]2x=9 /:2 lub 2x=1 /:2[/latex] [latex]x=4,5 lub x=0,5 otin D[/latex] =========================== [latex]log _{sqrt{3-x}} 0,25=-2[/latex] Dziedzina: [latex]sqrt{3-x}>0 Rightarrow 3-x>0 Rightarrow x<3[/latex] [latex]sqrt{3-x} eq 1 Rightarrow 3-x eq 1 Rightarrow x eq 2[/latex] [latex]sqrt{3-x}^{-2}=0,25[/latex] [latex]sqrt{3-x}^{-2}=0,5^2[/latex] [latex]sqrt{3-x}^{-2}=2^{-2}[/latex] [latex]sqrt{3-x}=2 /()^2[/latex] [latex]3-x=4[/latex] [latex]-x=4-3[/latex] [latex]-x=1 /:(-1)[/latex] [latex]x=-1[/latex]

Oblicz: a. log [latex]sqrt[3]{3} } [/latex] [latex]9 sqrt{3} [/latex] b. log[latex] frac{1}{5} [/latex] [latex]5 sqrt{5} [/latex] c. log[latex] frac{1}{6} [/latex][latex]36 sqrt[4]{6} [/latex] d. log[latex] sqrt{3} [/latex] [latex]27 sqrt[4]{3} [/late

Oblicz: a. log [latex]sqrt[3]{3} } [/latex] [latex]9 sqrt{3} [/latex] b. log[latex] frac{1}{5} [/latex] [latex]5 sqrt{5} [/latex] c. log[latex] frac{1}{6} [/latex][latex]36 sqrt[4]{6} [/latex] d. log[latex] sqrt{3} [/latex] [latex]27 sqrt[4]{3} ...

Oblicz : [latex] 441^{ frac{1}{2} } [/latex] [latex] 81^{ frac{1}{4} } [/latex] [latex]125^{ -frac {2}{3} } [/latex] [latex] frac{8}{27} ^{- frac{2}{3}} [/latex] [latex] 5^{ pi+3} : 5^{ pi } [/latex] [latex] log_{ frac{1}{3} } 3[/latex] [latex]

Oblicz : [latex] 441^{ frac{1}{2} } [/latex] [latex] 81^{ frac{1}{4} } [/latex] [latex]125^{ -frac {2}{3} } [/latex] [latex] frac{8}{27} ^{- frac{2}{3}} [/latex] [latex] 5^{ pi+3} : 5^{ pi } [/latex] [latex] log_{ frac{1}{3} } 3[/latex] [l...

Oblicz a [latex]log_{ frac{1}{8} } 64[/latex] b) [latex] logfrac{1}{2} 2 sqrt{2} [/latex] c)[latex] log_{ sqrt{2} } 0,125[/latex]

Oblicz a [latex]log_{ frac{1}{8} } 64[/latex] b) [latex] logfrac{1}{2} 2 sqrt{2} [/latex] c)[latex] log_{ sqrt{2} } 0,125[/latex]...

Zad. 1 Uzupełnij zapisy: a) [latex]log_{c}h=g extless --- extgreater _______________________[/latex] b) [latex]log_{c}k+log_{c}p= _______________________[/latex] Zad. 2 Oblicz: a) [latex]27^{frac{1}{3}}+5^{-2}= [/latex] b) [latex]frac{(17^{4})^{

Zad. 1 Uzupełnij zapisy: a) [latex]log_{c}h=g extless --- extgreater _______________________[/latex] b) [latex]log_{c}k+log_{c}p= _______________________[/latex] Zad. 2 Oblicz: a) [latex]27^{frac{1}{3}}+5^{-2}= [/latex] b) [latex]frac{(17...

Oblicz: a)[latex]125^{frac{1}{3}[/latex] b)[latex](7^{sqrt{2}})^{sqrt{2}}[/latex] c)[latex](frac{16}{81})^{frac{1}{4}}[/latex] d)[latex]5^{3+4sqrt7}} *(frac{1}{25})^{2sqrt{7}}[/latex] e)[latex]log_{2}6+log_{2}12+log_{2}frac{4}{9}[/latex]

Oblicz: a)[latex]125^{frac{1}{3}[/latex] b)[latex](7^{sqrt{2}})^{sqrt{2}}[/latex] c)[latex](frac{16}{81})^{frac{1}{4}}[/latex] d)[latex]5^{3+4sqrt7}} *(frac{1}{25})^{2sqrt{7}}[/latex] e)[latex]log_{2}6+log_{2}12+log_{2}frac{4}{9}[/latex]...