\(5^{x+1}-5^x=100\cdot25^{29}\)
\(\Rightarrow5^x\left(5-1\right)=100\cdot\left(5^2\right)^{29}\)
\(\Rightarrow5^x\cdot4=100\cdot5^{58}\)
\(\Rightarrow5^x=\dfrac{100\cdot5^{58}}{4}\)
\(\Rightarrow5^x=25\cdot5^{58}\)
\(\Rightarrow5^x=5^{60}\)
\(\Rightarrow x=60\)
\(5^{x+1}-5x=100.25^{29}\)
\(5.5^x-5^x=4.25.25^{29}\)
\(5^x.\left(5-1\right)4.25^{30}\)
\(4.5^x-4.\left(5^2\right)^{30}\)
\(5x=5^{60}\)
\(x=60\)
\(5^{x+1}-5^x=100.25^{29}\)
\(5^x.5-5^x=\left(5^2\right)^{29}.100\)
\(5^x.\left(5-1\right)=5^{2.29}.100\)
\(5^x.4=5^{58}.100\)
\(5^x=5^{58}.100:4\)
\(5^x=5^{58}.25\)
\(5^x=5^{58}.5^2\)
\(5^x=5^{60}\)
\(\Rightarrow x=60\)
\(5^{x+1}-5^x=100.25^{29}\)
\(5^x.\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)
\(5^x.4=4.5^{2+2.59}\)
\(5^x=4.5^{60}:4\)
\(5^x=5^{60}\)
\(x=60\)
