Find the value of (5 x+1)/3, if 25^4 x-3=5^6 x+8

$25^{4 x-3}=5^{6 x+8}$

= $5^{8 x-6}=5^{6 x+8}$

If the base is same of any multiple terms then we can put powers equal.

So, 8 x-6 = 6 x+8

= 2x = 14

x = 7

Put the value of x in $\frac{5 x+1}{3}$

= $\frac{5 (7)+1}{3}$ = 12