Hi
4*2^{x-1} - 3^x + 13*3^{x-1} = 6*2^{x+1} - 10*2^{x-2}
2*2^x - 3^x + 13/3*3^x = 12*2^x - 2.5*2^x
10/3*3^x = 7.5*2^x
log(10/3*3^x) = log(7.5*2^x)
log(10/3) + x log(3) = log(7.5) + x log(2)
x(log(3) - log(2)) = log(7.5) - log(10/3)
x(log(3) - log(2)) = log(15/2) - log(10/3)
x(log(3) - log(2)) = log((15/2)/(10/3))
x(log(3) - log(2)) = log(45/20)
x = log(45/20)/(log(3) - log(2))
x = 2
2^{5x-4} +3*2^{5x-9} +3*5^{5x-8} = 5^{5x-7} + 5*2^{5x-8}
2^{5x}/2^4 + 3*2^{5x}/2^9 + 3*5^{5x}/5^8 = 5^{5x}/5^7 + 5*2^{5x}/2^8
2^{5x}( 1/2^4 + 3/2^9 - 5/2^8) = 5^{5x}(1/5^7 - 3/5^8)
25/512 * 2^{5x} = 5^{5x}*(2/390625)
log(25/512 * 2^{5x}) = log(5^{5x}*(2/390625))
log(25/512) + 5x log(2) = 5x log(5) + log(2/390625)
5x(log(2) - log(5)) = log(2/390625) - log(25/512)
5x(log(2) - log(5)) = log(1024/9765625)
x = log(1024/9765625)/(5(log(2) - log(5)))
x = 2