To solve this equation, we will first simplify the terms using the properties of logarithms.

Apply the power rule: log(a^n) = n log(a)
5 log(2) x - 3 log(7) 49 = 2 log(2) x
log(2^5x) - log(7^3 49) = log(2^2x)
log(32x) - log(2401) = log(4x)

Apply the product rule: log(a) - log(b) = log(a/b)
log(32x/2401) = log(4x)

Simplify the expression inside the logarithm:
log(32x/2401) = log(4x)
log(32x/2401) = log(4x)
32x/2401 = 4x

Solve for x:
32x = 4x*2401
32x = 9604x
9604x - 32x = 0
9572x = 0
x = 0

Therefore, the solution to the equation 5 log(2) x - 3 log(7) 49 = 2 log(2) x is x = 0.