Logarithm Help?

Question

Solve for N in terms of X: (all logs are base 10)

8 log N = log x^(3/2) + log 2 - 1/2 log x + log x^3 - log 2/x^4

Answer 1

8 log N = log x^(3/2) + log 2 - 1/2 log x + log x^3 - log 2/x^4
log N^8 = (log x^(3/2) + log 2 - 1/2 log x ) + (log x^3 - log 2/x^4)
log N^8 = log [x^(3/2) * 2] / x^1/2 + log x^3 / [ 2/x^4]
log N^8 = log [2x^(3/2) ] / x^1/2 + log [x^7] / 2
log N^8 = log 2x + log x^7/ 2
log N^8 = log 2x * x^7/ 2
log N^8 = log x^8

so x=N