Bài tập 2.47 trang 124 SBT Toán 12

Bài tập 2.47 trang 124 SBT Toán 12

a)

\(\begin{array}{l}

{2^{x + 4}} + {2^{x + 2}} = {5^{x + 1}} + {3.5^x}\\

 \Leftrightarrow 16.{\left( {\frac{2}{5}} \right)^x} + 4.{\left( {\frac{2}{5}} \right)^x} = 5 + 3\\

 \Leftrightarrow 20.{\left( {\frac{2}{5}} \right)^x} = 8 \Leftrightarrow {\left( {\frac{2}{5}} \right)^x} = \frac{2}{5}\\

 \Leftrightarrow x = 1

\end{array}\)

b) 

\(\begin{array}{l}

{5^{2x}} - {7^x} - {5^{2x}}.17 + {7^x}.17 = 0\\

 \Leftrightarrow {16.7^x} - {16.5^x} = 0\\

 \Leftrightarrow {7^x} = {5^x} \Leftrightarrow x = 0

\end{array}\)

c) 

\(\begin{array}{l}

{4.9^x} + {12^x} - {3.16^x} = 0\\

 \Leftrightarrow 4.{\left( {\frac{9}{{12}}} \right)^x} - 3.{\left( {\frac{{16}}{{12}}} \right)^x} + 1 = 0\\

 \Leftrightarrow 4.{\left( {\frac{3}{4}} \right)^x} - 3.{\left( {\frac{4}{3}} \right)^x} + 1 = 0\\

 \Leftrightarrow 4.{\left( {\frac{3}{4}} \right)^{2x}} + {\left( {\frac{3}{4}} \right)^x} - 3 = 0\\

 \Leftrightarrow \left[ \begin{array}{l}

{\left( {\frac{3}{4}} \right)^x} =  - 1\,\,\left( l \right)\\

{\left( {\frac{3}{4}} \right)^x} = \frac{3}{4}

\end{array} \right. \Leftrightarrow x = 1

\end{array}\)

d) 

\(\begin{array}{l}

 - {8^x} + {2.4^x} + {2^x} - 2 = 0\\

 \Leftrightarrow  - {2^{3x}} + {2.2^{2x}} + {2^x} - 2 = 0\\

 \Leftrightarrow \left[ \begin{array}{l}

{2^x} = 1\\

{2^x} =  - 1\,\,\left( l \right)\\

{2^x} = 1

\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}

x = 0\\

x = 1

\end{array} \right.

\end{array}\)

-- Mod Toán 12