\(7^x.7^2+7^x=17150\)
\(\Leftrightarrow7^x\left(7^2+1\right)=17150\)
\(\Leftrightarrow7^x.50=17150\)
\(\Leftrightarrow7^x=17150:50\)
\(\Leftrightarrow7^x=343\)
\(\Leftrightarrow7^x=7^3\)
\(\Leftrightarrow x=3\)
7\(^x\).72+7\(^x\)=171507\(^x\).72+7\(^x\)=17150
7\(^{x^{ }}\)(72+1)=17150⇔7\(^x\)(72+1)=17150
7\(^x\).50=17150⇔7\(^x\).50=17150
7\(x\)=17150:50⇔7\(^x\)=17150:50
7\(^x\)=343⇔7\(^x\)=343
7\(^x\)=73⇔7\(^x\)=73
x=3