Ecuatie puteri

Elena09 Sam Iun 02, 2012 2:36 pm

Sa se rezolve ecuatia: $2^{2x+2}\cdot 10^{x}=2^{3x}\cdot 5^{x}+120$

**Admin** Sam Iun 02, 2012 8:51 pm

$\begin{array}{l} {2^{2x + 2}} \times {10^x} = {2^{3x}} \times {5^x} + 120 \Leftrightarrow {2^{2x + 2}} \times \underbrace {{2^x} \times {5^x}}_{ = {{10}^x}} = {2^{3x}} \times {5^x} + 120 \Leftrightarrow {2^2} \times {2^{3x}} \times {5^x} = {2^{3x}} \times {5^x} + 120\\ {\text{Notam}}:y = {2^{3x}} \times {5^x} \Rightarrow 4y = y + 120 \Rightarrow y = 40 \Rightarrow {2^{3x}} \times {5^x} = 40 \Leftrightarrow {\left( {8 \times 5} \right)^x} = 40 \Rightarrow x = {\log _{40}}40 = 1 \end{array}$
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