A)1/9.3^4.3^n+1=9^4 B)1/2.2^n +4.2^n=9.2^5 C)5^-3.25^n=5^3n

Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
A)\\
\dfrac{1}{9}{.3^4}{.3^{n + 1}} = {9^4}\\
 \Leftrightarrow {3^4}{.3^{n + 1}} = {9.9^4}\\
 \Leftrightarrow {3^{4 + \left( {n + 1} \right)}} = {9^5}\\
 \Leftrightarrow {3^{n + 5}} = {\left( {{3^2}} \right)^5}\\
 \Leftrightarrow {3^{n + 5}} = {3^{10}}\\
 \Leftrightarrow n + 5 = 10\\
 \Leftrightarrow n = 5\\
B)\\
\dfrac{1}{2}{.2^n} + {4.2^n} = {9.2^5}\\
 \Leftrightarrow {2^n} + {2.4.2^n} = {2.9.2^5}\\
 \Leftrightarrow {2^n} + {8.2^n} = {9.2^6}\\
 \Leftrightarrow {9.2^n} = {9.2^6}\\
 \Leftrightarrow {2^n} = {2^6}\\
 \Leftrightarrow n = 6\\
C)\\
{5^{ – 3}}{.25^n} = {5^{3n}}\\
 \Leftrightarrow {5^{ – 3}}.{\left( {{5^2}} \right)^n} = {5^{3n}}\\
 \Leftrightarrow {5^{ – 3}}{.5^{2n}} = {5^{3n}}\\
 \Leftrightarrow {5^{ – 3 + 2n}} = {5^{3n}}\\
 \Leftrightarrow  – 3 + 2n = 3n\\
 \Leftrightarrow n =  – 3
\end{array}\)