How do you solve log47+2log4x=log42?

1 Answer
Dec 14, 2015

x=27

Explanation:

Given:
XXXlog4(7)+2log4(x)=log4(2)

Remember
XXXlog multiplication rule: logb(pq)=logb(p)+logb(q)
XXXlog power rule: logb(st)=tlogb(s)

Therefore the given equation can be rewritten as
XXXlog4(7x2)=log4(2)

from which it follows that
XXX7x2=2

XXXx2=27

XXXx=27
XXXXXXwe can ignore the negative root as extraneous since x requires x0 for Real solutions