Question

\(b) 5^{x+4} - 3 . 5^{x+3} = 2. 5^{11} \)

\(c) 2 . 3^{x+2} + 4 . 3^{x+1} = 10 . 3 ^{6}\)

\(d) 6 . 8 ^ {x-1} + 8 ^ {x+1} = 6 . 8^ {19} + 8 ^ {21}\)

Answer 1

b) Ta có: \(5^{x+4}-3\cdot5^{x+3}=2\cdot5^{11}\)

\(\Leftrightarrow2\cdot5^{x+3}=2\cdot5^{11}\)

\(\Leftrightarrow x+3=11\)

hay x=8

c) Ta có: \(2\cdot3^{x+2}+4\cdot3^{x+1}=10\cdot3^6\)

\(\Leftrightarrow18\cdot3^x+12\cdot3^x=10\cdot3^6\)

\(\Leftrightarrow30\cdot3^x=30\cdot3^5\)

Suy ra: x=5

d) Ta có: \(6\cdot8^{x-1}+8^{x+1}=6\cdot8^{19}+8^{21}\)

\(\Leftrightarrow6\cdot\dfrac{8^x}{8}+8^x\cdot8=6\cdot8^{19}+64\cdot8^{19}\)

\(\Leftrightarrow8^x\cdot\dfrac{35}{4}=70\cdot8^{19}\)

\(\Leftrightarrow8^x=8^{20}\)

Suy ra: x=20