logarytmy  1. wiadomo że log(a)81=log(5)b=2 Oblicz pierwiastek a+b 2.wiadomo że log (a)16=log(3)b=2 Oblicz pierwiastek a*b 3.Jeżeli.. log(2)a=1 i log(3)b = log(5)c = 2 to wartość wyrażenia pierwiastek a+b+c jest równa ile?

1. [latex]log_a81=log_5b=2[/latex] [latex]a eq 1,a>0[/latex] [latex]b>0[/latex] ---------------- [latex]log_a81=2[/latex] [latex]a^2=81[/latex] [latex]a= sqrt{81}[/latex] [latex]a=9[/latex] ---------------- [latex]log_5b=2[/latex] [latex]5^2=b[/latex] [latex]b=25[/latex] ---------------- [latex]sqrt{a+b}= sqrt{9+25}= sqrt{34}[/latex] ===================== 2. [latex]log_a16=log_3b=2[/latex] [latex]a eq 1,a>0[/latex] [latex]b>0[/latex] ---------------- [latex]log_a16=2[/latex] [latex]a^2=16[/latex] [latex]a= sqrt{16}[/latex] [latex]a=4[/latex] ---------------- [latex]log_3b=2[/latex] [latex]3^2=b[/latex] [latex]b=9[/latex] ---------------- [latex]sqrt{acdotb}= sqrt{4cdot 9}= sqrt{36}=6[/latex] ===================== 3. [latex]log_2a=1[/latex] [latex]log_3b = log_5c = 2[/latex] [latex]a>0, b>0,c>0[/latex] ---------------- [latex]log_2a=1[/latex]   [latex]2^1=a[/latex] [latex]a=2[/latex] ---------------- [latex]log_3b = 2[/latex] [latex]3^2=b[/latex] [latex]b=9[/latex] ---------------- [latex]log_5c = 2[/latex] [latex]5^2=c[/latex] [latex]c=25[/latex] ---------------- [latex]sqrt{a+b+c}= sqrt{2+9+25}= sqrt{36}=6[/latex]