задачки закачки

[darthmol]

част едно Логаритми:
пресмeтнете:
log1/16 8
log1/9 \sqrt[3]{81}
10^3log2
81^log92

решете уравнението:
5^x2 - 2x = 6^x2 - 2x
8.7^x2 - 3x + 3 = 7.8^x2 - 3x + 3

ако може като за n00b
благодаря ти предварително!

[ammornil]

Част1)
[tex]log_{\frac{1}{16}}8=\frac{log_{2}8}{log_{2}\frac{1}{16}}=\frac{log_{2}2^{3}}{log_{2}2^{-4}}=\frac{3}{-4}=-\frac{3}{4}[/tex]


[tex]log_{\frac{1}{9}}\sqrt[3]{81} =\frac{log_{3}(81)^{\frac{1}{3}}}{log_{3}\frac{1}{9}}=\frac{log_{3}(3^{4})^{\frac{1}{3}}}{log_{3}3^{-2}}=\frac{\frac{4}{3}}{-2}=-\frac{2}{3}[/tex]


[tex]10^{3lg2}=10^{lg(2^{3})}=2^{3}=8[/tex]


[tex]81^{log_{9}2}=(9^{2})^{log_{9}2}=9^{2.log_{9}2}=9^{log_{9}2^{2}}=2^{2}=4[/tex]
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[ammornil]

[tex]5^{x^{2}} \cancel{-2.x}=6^{x^{2}}\cancel{-2.x} \Leftrightarrow 5^{x^{2}}=6^{x^{2}} |:5^{x^{2}}\ne0[/tex]

[tex]\frac{6^{x^{2}}}{5^{x^{2}}}=1 \Leftrightarrow \left(\frac{6}{5}\right)^{x^{2}}=\left(\frac{6}{5}\right)^{0} \Leftrightarrow x^{2}=0 \Rightarrow x=0[/tex]

[ammornil]

[tex]8.7^{x^{2}} \cancel{-3.x}\cancel{+3}=7.8^{x^{2}}\cancel{-3.x}\cancel{+3} \Leftrightarrow 8.7^{x^{2}}=7.8^{x^{2}} |:7.7^{x^{2}} \ne0[/tex]

[tex]\frac{8}{7}=\frac{8^{x^{2}}}{7^{x^{2}}} \Leftrightarrow \left(\frac{8}{7}\right)^{1}=\left(\frac{8}{7}\right)^{x^{2}}[/tex]

[tex]x^{2}=1 \Rightarrow x=\pm1[/tex]

[tex]x_{1}=-1[/tex] ; [tex]x_{2}=1[/tex]

[darthmol]

благодаря ти!