Question

solve
log4(8log2 (x)=2

Answer 1

First, I'll expand the square on the right-hand side to be the explicit product of two logs:log2(x2) = [log2(x)]2log2(x2) = [log2(x)] [log2(x)]Then I'll apply the log rule to move the "squared" from inside the log on the left-hand side of the equation, taking it out in front of that log as a multiplier:2·log2(x) = [log2(x)] [log2(x)]Then I'll move that term from theleft-hand side of the equation to the right-hand side:0 = [log2(x)] [log2(x)] – 2·log2(x)This equation may look bad, but take a close look. It's nothing more than a factoring exercise at this point. So I'll factor, and then I'll solve the factors by using The Relationship:0 = [log2(x)] [log2(x) – 2]log2(x) = 0orlog2(x) – 2 = 020=xorlog2(x) = 21 =xor22=x1 =xor4 =xThen my solution is:x= 1,