Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
*)\\
{2^x} = {4^6}{.16^3}\\
\Leftrightarrow {2^x} = {\left( {{2^2}} \right)^6}.{\left( {{2^4}} \right)^3}\\
\Leftrightarrow {2^x} = {2^{12}}{.2^{12}}\\
\Leftrightarrow {2^x} = {2^{24}}\\
\Leftrightarrow x = 24\\
*)\\
{2^x} = {4^4}{.2^3}\\
\Leftrightarrow {2^x} = {\left( {{2^2}} \right)^4}{.2^3}\\
\Leftrightarrow {2^x} = {2^8}{.2^3}\\
\Leftrightarrow {2^x} = {2^{11}}\\
\Leftrightarrow x = 11\\
*)\\
{2^x} = {4^5}{.16^2}\\
\Leftrightarrow {2^x} = {\left( {{2^2}} \right)^5}.{\left( {{2^4}} \right)^2}\\
\Leftrightarrow {2^x} = {2^{10}}{.2^8}\\
\Leftrightarrow {2^x} = {2^{18}}\\
\Leftrightarrow x = 18\\
*)\\
{2^x} = {2^5}{.2^6}\\
\Leftrightarrow {2^x} = {2^{11}}\\
\Leftrightarrow x = 11\\
*)\\
{2^x} = {16^5}{.32^3}\\
\Leftrightarrow {2^x} = {\left( {{2^4}} \right)^5}.{\left( {{2^5}} \right)^3}\\
\Leftrightarrow {2^x} = {2^{20}}{.2^{15}}\\
\Leftrightarrow {2^x} = {2^{35}}\\
\Leftrightarrow x = 35\\
*)\\
{2^x} = {32^5}{.64^6}\\
\Leftrightarrow {2^x} = {\left( {{2^5}} \right)^5}.{\left( {{2^6}} \right)^6}\\
\Leftrightarrow {2^x} = {2^{25}}{.2^{36}}\\
\Leftrightarrow {2^x} = {2^{61}}\\
\Leftrightarrow x = 61\\
*)\\
{2^x} = {4^3}{.8^4}{.16^5}\\
\Leftrightarrow {2^x} = {\left( {{2^2}} \right)^3}.{\left( {{2^3}} \right)^4}.{\left( {{2^4}} \right)^5}\\
\Leftrightarrow {2^x} = {2^6}{.2^{12}}{.2^{20}}\\
\Leftrightarrow {2^x} = {2^{38}}\\
\Leftrightarrow x = 38\\
*)\\
{3^x} = {9^{ - 6}}{.27^{ - 5}}{.81^8}\\
\Leftrightarrow {3^x} = {\left( {{3^2}} \right)^{ - 6}}.{\left( {{3^3}} \right)^{ - 5}}.{\left( {{3^4}} \right)^8}\\
\Leftrightarrow {3^x} = {3^{ - 12}}{.3^{ - 15}}{.3^{32}}\\
\Leftrightarrow {3^x} = {3^5}\\
\Leftrightarrow x = 5\\
*)\\
{2^x} = {8^3}{.8^{ - 10}}{.8^3}\\
\Leftrightarrow {2^x} = {8^{ - 4}}\\
\Leftrightarrow {2^x} = {\left( {{2^3}} \right)^{ - 4}}\\
\Leftrightarrow {2^x} = {2^{ - 12}}\\
\Leftrightarrow x = - 12
\end{array}\)
