Bài tập 2.67 trang 133 SBT Toán 12

Bài tập 2.67 trang 133 SBT Toán 12

a)

\(\begin{array}{l}
{9^x} - {3^x} - 6 = 0\\
 \Leftrightarrow {3^{2x}} - 3x - 6 = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
{3^x} =  - 2\,\,(l)\\
{3^x} = 3
\end{array} \right. \Leftrightarrow x = 1
\end{array}\)

b)

\(\begin{array}{l}
{e^{2x}} - {3^{ex}} - 4 + 12{e^{ - x}} = 0\\
 \Leftrightarrow {e^{2x}} - 3{e^x} - 4 + \frac{{12}}{{{e^x}}} = 0\\
 \Rightarrow {e^{3x}} - 3{e^{2x}} - 4{e^x} + 12 = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
{e^x} =  - 2\,\,\left( l \right)\\
{e^x} = 2\\
{e^x} = 3
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \ln 2\\
x = \ln 3
\end{array} \right.
\end{array}\)

c)

\(\begin{array}{l}
{3.4^x} + \frac{1}{3}{.9^{x + 2}} = {6.4^{x + 1}} - \frac{1}{2}{.9^{x + 1}}\\
 \Leftrightarrow {3.4^x} - {24.4^x} + {27.9^x} + \frac{9}{2}{.9^x} = 0\\
 \Leftrightarrow \frac{{63}}{2}{.9^x} = {21.4^x}\\
 \Leftrightarrow {\left( {\frac{9}{4}} \right)^x} = \frac{2}{3}\\
 \Leftrightarrow x =  - \frac{1}{2}
\end{array}\)

d)

\(\begin{array}{l}
{2^{{x^2} - 1}} - 3{x^2} = {3^{{x^2} - 1}} - {2^{{x^2} + 2}}\\
 \Leftrightarrow \frac{1}{2}{.2^{{x^2}}} - {3^{{x^2}}} = \frac{1}{3}{.3^{{x^2}}} - {4.2^{{x^2}}}\\
 \Leftrightarrow \frac{9}{2}{.2^{{x^2}}} = \frac{4}{3}{.3^{{x^2}}}\\
 \Rightarrow {\left( {\frac{2}{3}} \right)^{{x^2}}} = \frac{8}{{27}}\\
 \Leftrightarrow {x^2} = 3\\
 \Leftrightarrow x =  \pm \sqrt 3 
\end{array}\)

-- Mod Toán 12