Question

Solve the equation $5^2\cdot 5^4\cdot 5^6.......{.5}^{2x}=(0.04{)}^{-28}$

Answer 1

$5^2\cdot 5^4\cdot 5^6.......{.5}^{2x}=(0.04{)}^{-28}$

$5^{2+4+6+......+2x}=(\frac{1}{25}{)}^{-28}$

$5^{2(1+2+3+.....+x)}=5^{28\times 2}$

$x(x+1)=56=7\times 8$

$x=7$