Question

7^3x+9*5^2x =5^2x+9*7^3x

Answer 1

$7^{3x}+9\cdot 5^{2x}=5^{2x}+9\cdot 7^{3x}\\\\9\cdot 5^{2x}-5^{2x}=9\cdot 7^{3x}-7^{3x}\\\\5^{2x}\cdot (9-1)=7^{3x}\cdot (9-1)\\\\8\cdot 5^{2x}=8\cdot 7^{3x}~~~~~~~\Big|:8$

$5^{2x}=7^{3x}~~~~~~~\Big|\log_7()\\\\\log_7 \Big(5^{2x}\Big)=\log_7\Big(7^{3x}\Big)\\\\2x\cdot \log_7 5=3x\\\\x\cdot \Big(2\log_7 5-3\Big)=0\\\\2\log_7 5-3\neq0;\ \ \ \ \boxed{\boldsymbol{x=0}}$