Logarithms, please help.

Remember  log (a/b) = log a - log b  

    and  log (ab) = log a + log b

So:

Log₇x + logy - log₇z=  log₇ (xy/z)

e^4/3ln2-1 =  e^4/3ln2 (e^-1) = e^{ln2^4/3} /e   = 2^(4/3)/e = \(\sqrt[3]{2^4}\)   / e =  2\(\sqrt[3]{2}\) / e

You should be able to see their errors.....