Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
{8^{x + 1}} = {16^6}\\
\Leftrightarrow {\left( {{2^3}} \right)^{x + 1}} = {\left( {{2^4}} \right)^6}\\
\Leftrightarrow {2^{3x + 3}} = {2^{24}}\\
\Leftrightarrow 3x + 3 = 24\\
\Leftrightarrow x = 7\\
b,\\
{5^x}{.25^3} = {125^3}\\
\Leftrightarrow {5^x}.{\left( {{5^2}} \right)^3} = {\left( {{5^3}} \right)^3}\\
\Leftrightarrow {5^x}{.5^6} = {5^9}\\
\Leftrightarrow {5^{x + 6}} = {5^9}\\
\Leftrightarrow x + 6 = 9\\
\Leftrightarrow x = 3\\
c,\\
{7^{5x}}:49 = {7^{28}}\\
\Leftrightarrow {7^{5x}}:{7^2} = {7^{28}}\\
\Leftrightarrow {7^{5x - 2}} = {7^{28}}\\
\Leftrightarrow 5x - 2 = 28\\
\Leftrightarrow 5x = 30\\
\Leftrightarrow x = 6\\
d,\\
{2^x} - 5 = 27\\
\Leftrightarrow {2^x} = 32\\
\Leftrightarrow {2^x} = {2^5}\\
\Leftrightarrow x = 5\\
e,\\
{2^{x + 1}} + {4.2^x} = {3.2^7}\\
\Leftrightarrow {2^{x + 1}} + {2^2}{.2^x} = {3.2^7}\\
\Leftrightarrow {2^{x + 1}} + {2.2^{x + 1}} = {3.2^7}\\
\Leftrightarrow {2^{x + 1}}.\left( {1 + 2} \right) = {3.2^7}\\
\Leftrightarrow {3.2^{x + 1}} = {3.2^7}\\
\Leftrightarrow x + 1 = 7\\
\Leftrightarrow x = 6
\end{array}\)
