Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
*)\\
{3.5^{2x + 1}} - {3.25^x} = 300\\
 \Leftrightarrow {3.5^{2x}}{.5^1} - {3.25^x} = 300\\
 \Leftrightarrow 3.5.{\left( {{5^2}} \right)^x} - {3.25^x} = 300\\
 \Leftrightarrow {15.25^x} - {3.25^x} = 300\\
 \Leftrightarrow {25^x}.\left( {15 - 3} \right) = 300\\
 \Leftrightarrow {25^x}.12 = 300\\
 \Leftrightarrow {25^x} = 300:12\\
 \Leftrightarrow {25^x} = 25\\
 \Leftrightarrow x = 1\\
*)\\
{\left( {3x - 2} \right)^4} = 625\\
 \Leftrightarrow {\left( {3x - 2} \right)^4} = {5^4}\\
 \Leftrightarrow 3x - 2 = 5\\
 \Leftrightarrow 3x = 5 + 2\\
 \Leftrightarrow 3x = 7\\
 \Leftrightarrow x = \frac{7}{3}\\
*)\\
{\left( {x - 8} \right)^6} = \left( {x - 8} \right)\\
 \Leftrightarrow {\left( {x - 8} \right)^6} - \left( {x - 8} \right) = 0\\
 \Leftrightarrow \left( {x - 8} \right).\left[ {{{\left( {x - 8} \right)}^5} - 1} \right] = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
x - 8 = 0\\
{\left( {x - 8} \right)^5} - 1 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 8\\
{\left( {x - 8} \right)^5} = 1
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 8\\
x - 8 = 1
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 8\\
x = 9
\end{array} \right.\\
*)\\
{\left( {2x - 1} \right)^2} = {\left( {x - 4} \right)^2}\\
 \Leftrightarrow 2x - 1 = x - 4\\
 \Leftrightarrow 2x - x =  - 4 + 1\\
 \Leftrightarrow x =  - 3\\
*)\\
{6^{x + 6}} = {36^{x + 2}}\\
 \Leftrightarrow {6^{x + 6}} = {\left( {{6^2}} \right)^{x + 2}}\\
 \Leftrightarrow {6^{x + 6}} = {6^{2.\left( {x + 2} \right)}}\\
 \Leftrightarrow {6^{x + 6}} = {6^{2x + 4}}\\
 \Leftrightarrow x + 6 = 2x + 4\\
 \Leftrightarrow 6 - 4 = 2x - x\\
 \Leftrightarrow 2 = x\\
 \Rightarrow x = 2
\end{array}\)

Đáp án:

≡.≡

Giải thích các bước giải:

\begin{array}{l} *)\\ {3.5^{2x + 1}} - {3.25^x} = 300\\  \Leftrightarrow {3.5^{2x}}{.5^1} - {3.25^x} = 300\\  \Leftrightarrow 3.5.{\left( {{5^2}} \right)^x} - {3.25^x} = 300\\  \Leftrightarrow {15.25^x} - {3.25^x} = 300\\  \Leftrightarrow {25^x}.\left( {15 - 3} \right) = 300\\  \Leftrightarrow {25^x}.12 = 300\\  \Leftrightarrow {25^x} = 300:12\\  \Leftrightarrow {25^x} = 25\\  \Leftrightarrow x = 1\\ *)\\ {\left( {3x - 2} \right)^4} = 625\\  \Leftrightarrow {\left( {3x - 2} \right)^4} = {5^4}\\  \Leftrightarrow 3x - 2 = 5\\  \Leftrightarrow 3x = 5 + 2\\  \Leftrightarrow 3x = 7\\  \Leftrightarrow x = \frac{7}{3}\\ *)\\ {\left( {x - 8} \right)^6} = \left( {x - 8} \right)\\  \Leftrightarrow {\left( {x - 8} \right)^6} - \left( {x - 8} \right) = 0\\  \Leftrightarrow \left( {x - 8} \right).\left[ {{{\left( {x - 8} \right)}^5} - 1} \right] = 0\\  \Leftrightarrow \left[ \begin{array}{l} x - 8 = 0\\ {\left( {x - 8} \right)^5} - 1 = 0 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 8\\ {\left( {x - 8} \right)^5} = 1 \end{array} \right.\\  \Leftrightarrow \left[ \begin{array}{l} x = 8\\ x - 8 = 1 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 8\\ x = 9 \end{array} \right.\\ *)\\ {\left( {2x - 1} \right)^2} = {\left( {x - 4} \right)^2}\\  \Leftrightarrow 2x - 1 = x - 4\\  \Leftrightarrow 2x - x =  - 4 + 1\\  \Leftrightarrow x =  - 3\\ *)\\ {6^{x + 6}} = {36^{x + 2}}\\  \Leftrightarrow {6^{x + 6}} = {\left( {{6^2}} \right)^{x + 2}}\\  \Leftrightarrow {6^{x + 6}} = {6^{2.\left( {x + 2} \right)}}\\  \Leftrightarrow {6^{x + 6}} = {6^{2x + 4}}\\  \Leftrightarrow x + 6 = 2x + 4\\  \Leftrightarrow 6 - 4 = 2x - x\\  \Leftrightarrow 2 = x\\  \Rightarrow x = 2 \end{array}