Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
{5^{x + 1}}.2 + {5^{x + 2}}.3 = 425\\
\Leftrightarrow {5^{x + 1}}.2 + {5.5^{x + 1}}.3 = 425\\
\Leftrightarrow {5^{x + 1}}.\left( {2 + 5.3} \right) = 425\\
\Leftrightarrow {5^{x + 1}}.17 = 425\\
\Leftrightarrow {5^{x + 1}} = 25\\
\Leftrightarrow {5^{x + 1}} = {5^2}\\
\Leftrightarrow x + 1 = 2\\
\Leftrightarrow x = 1\\
b,\\
{4^{x + 3}} + {4^{x + 2}} + {4^{x + 1}} + {4^x} = 1360\\
\Leftrightarrow {4^x}{.4^3} + {4^x}{.4^2} + {4^x}{.4^1} + {4^x} = 1360\\
\Leftrightarrow {4^x}.\left( {{4^3} + {4^2} + {4^1} + 1} \right) = 1360\\
\Leftrightarrow {4^x}.85 = 1360\\
\Leftrightarrow {4^x} = 16\\
\Leftrightarrow {4^x} = {4^2}\\
\Leftrightarrow x = 2\\
c,\\
{7^{x + 1}}.2 + {7^{x + 2}}.3 + {7^x} = 7938\\
\Leftrightarrow {7^x}{.7^1}.2 + {7^x}{.7^2}.3 + {7^x} = 7938\\
\Leftrightarrow {7^x}.\left( {{7^1}.2 + {7^2}.3 + 1} \right) = 7938\\
\Leftrightarrow {7^x}.162 = 7938\\
\Leftrightarrow {7^x} = 49\\
\Leftrightarrow {7^x} = {7^2}\\
\Leftrightarrow x = 2\\
d,\\
{3.6^x} + {6^{x + 2}} + {6^{x + 1}} = 1620\\
\Leftrightarrow {3.6^x} + {6^x}{.6^2} + {6^x}{.6^1} = 1620\\
\Leftrightarrow {6^x}.\left( {3 + {6^2} + {6^1}} \right) = 1620\\
\Leftrightarrow {6^x}.45 = 1620\\
\Leftrightarrow {6^x} = 36\\
\Leftrightarrow {6^x} = {6^2}\\
\Leftrightarrow x = 2
\end{array}\)
