Strona 1 z 1

Równania.

: 9 mar 2009, o 16:49
autor: Madzian
1. Rozwiąż równania:
a) \(\displaystyle{ 3^{x+2}}\) * \(\displaystyle{ 9^{3x-1}}\) = \(\displaystyle{ 27^{x+4}}\)
b) \(\displaystyle{ log_{2}}\)x = - \(\displaystyle{ \frac{2}{3}}\)
c) \(\displaystyle{ log_{x}}\) \(\displaystyle{ \frac{1}{9}}\) = -2


2. Oblicz:
d) \(\displaystyle{ 10^{2+log3}}\)
e) \(\displaystyle{ log_{\frac{1}{2}}\)32

Równania.

: 9 mar 2009, o 17:08
autor: kakaona
1.
a)
\(\displaystyle{ 3^{x+2} * 3^{2(3x-1)} = 3^{3(x+4)} \Leftrightarrow 3^{x+2} * 3^{6x-2} = 3^{3x+12} \Leftrightarrow 3^{7x} = 3^{3x+12} \Leftrightarrow 7x=3x+12 \Leftrightarrow 4x=12 \Leftrightarrow x=3}\)
b)
\(\displaystyle{ x = 2^{-\frac{2}{3}}\)
c)
\(\displaystyle{ x^{-2} = \frac{1}{9}}\)
\(\displaystyle{ x^{-2} = 3^{-2}}\)
\(\displaystyle{ x = 3}\)