Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\dfrac{1}{9}{.3^4}{.3^n} = {3^7}\\
\Leftrightarrow \dfrac{1}{{{3^2}}}{.3^4}{.3^n} = {3^7}\\
\Leftrightarrow {3^4}{.3^n} = {3^7}{.3^2}\\
\Leftrightarrow {3^{4 + n}} = {3^{7 + 2}}\\
\Leftrightarrow 4 + n = 7 + 2\\
\Leftrightarrow n = 5\\
b,\\
\dfrac{1}{2}{.2^n} + {4.2^n} = {9.2^5}\\
\Leftrightarrow {2^n}.\left( {\dfrac{1}{2} + 4} \right) = {9.2^5}\\
\Leftrightarrow {2^n}.\dfrac{9}{2} = {9.2^5}\\
\Leftrightarrow {2^n}.\dfrac{1}{2} = {2^5}\\
\Leftrightarrow {2^n} = {2^5}.2\\
\Leftrightarrow {2^n} = {2^6}\\
\Leftrightarrow n = 6\\
c,\\
\dfrac{1}{9}{.27^n} = {3^n}\\
\Leftrightarrow \dfrac{1}{{{3^2}}}.{\left( {{3^3}} \right)^n} = {3^n}\\
\Leftrightarrow {\left( {{3^3}} \right)^n} = {3^n}{.3^2}\\
\Leftrightarrow {3^{3n}} = {3^{n + 2}}\\
\Leftrightarrow 3n = n + 2\\
\Leftrightarrow 2n = 2\\
\Leftrightarrow n = 1\\
d,\\
{64.4^n} = {4^5}\\
\Leftrightarrow {4^3}{.4^n} = {4^5}\\
\Leftrightarrow {4^{3 + n}} = {4^5}\\
\Leftrightarrow 3 + n = 5\\
\Leftrightarrow n = 2\\
e,\\
{27.3^n} = 243\\
\Leftrightarrow {3^n} = 243:27\\
\Leftrightarrow {3^n} = 9\\
\Leftrightarrow n = 2\\
g,\\
{49.7^n} = 2401\\
\Leftrightarrow {7^n} = 2401:49\\
\Leftrightarrow {7^n} = 49\\
\Leftrightarrow {7^n} = {7^2}\\
\Leftrightarrow n = 2
\end{array}\)
