a) Ta có: \(3\cdot5^x=3\cdot5^4\)
\(\Leftrightarrow5^x=5^4\)
\(\Leftrightarrow x=4\)
Vậy: x=4
b) Ta có: \(9\cdot7^x=6\cdot7^5+3\cdot7^5\)
\(\Leftrightarrow9\cdot7^x=\left(6+3\right)\cdot7^5\)
\(\Leftrightarrow9\cdot7^x=9\cdot7^5\)
\(\Leftrightarrow7^x=7^5\)
\(\Leftrightarrow x=5\)
Vậy: x=5
c) Ta có: \(2\cdot3^{x+2}+4\cdot3^{x+1}=10\cdot3^7\)
\(\Leftrightarrow2\cdot3^{x+2}+2\cdot6^{x+1}=10\cdot3^7\)
\(\Leftrightarrow2\cdot\left(3^{x+2}+6^{x+1}\right)=10\cdot3^7\)
\(\Leftrightarrow3^{x+2}+6^{x+1}=\frac{10\cdot3^7}{2}\)
\(\Leftrightarrow3^{x+1}\cdot3+3^{x+1}\cdot2=5\cdot3^7\)
\(\Leftrightarrow3^{x+1}\cdot\left(3+2\right)=5\cdot3^7\)
\(\Leftrightarrow5\cdot3^{x+1}=5\cdot3^7\)
\(\Leftrightarrow3^{x+1}=3^7\)
\(\Leftrightarrow x+1=7\)
\(\Leftrightarrow x=6\)
Vậy: x=6
a) \(3.5^x=3.5^4\)
\(\Rightarrow3.5^x-3.5^4=0\)
\(\Rightarrow3.\left(5^x-5^4\right)=0\)
Vì \(3\ne0.\)
\(\Rightarrow5^x-5^4=0\)
\(\Rightarrow5^x=0+5^4\)
\(\Rightarrow5^x=5^4\)
\(\Rightarrow x=4\left(TM\right).\)
Vậy \(x=4.\)
Chúc bạn học tốt!
