# SOLUTION: simplify in terms of a single logarithm with base 4 {{{ log to the base 2 of (x)- log to the base 2 of (2/y)+ log to the base 8 of (sqrt( y ))- log to the base 16 of (z^2) }}}

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: simplify in terms of a single logarithm with base 4 {{{ log to the base 2 of (x)- log to the base 2 of (2/y)+ log to the base 8 of (sqrt( y ))- log to the base 16 of (z^2) }}}       Log On

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 Algebra: Logarithm Solvers Lessons Answers archive Quiz In Depth

 Question 605186: simplify in terms of a single logarithm with base 4 Answer by lwsshak3(6465)   (Show Source): You can put this solution on YOUR website!simplify in terms of a single logarithm with base 4. log to the base 2 of (x)- log to the base 2 of (2/y)+ log to the base 8 of (sqrt( y ))- log to the base 16 of (z^2) ** log4(x)/log4(2)-log4(2/y)/log4(2)+log4√y/log4(8)-log4(z^2)/log4(16) .. log4(2)=1/2 log4(8)=3/2 log4(16)=4 .. log4(x)/(1/2)-log4(2/y)/(1/2)+log4√y/(3/2)-log4(z^2)/4 2log4(x)-2log4(2/y)+(2/3)log4√y-4log4(z^2) rearrange terms 2log4(x)+(2/3)log4√y-(2log4(2/y)+4log4(z^2)) place under single log log4[x^2*y^(1/3)/(2/y)^2*z^8]