1)express 2Igsquarerootx-Ig4/3x^2+log(4x^3)/log(100) in the form aIgx+Igb, where a and b are constants.
2)If InK=Ina-Inb+Inc-t/bc, show that K=ac/b(e)^-t/bc
#1
I will interpret that as:
2log (squarerootx) -log (4/3x^2) + log(4x^3)/log(100)
= 2log x^(1/2) - (log4 - log3 - 2logx) + (log4 + 3logx)/2
= logx - log4 + log3 + 2logx + (1/2)log4 + (3/2)logx
= (9/2)logx - (1/2)log4
= (1/2)(9logx - log4)
or,
= (1/2) log(x^9/4)
= log [x^9/4]^(1/2)
or
= log [x^4 sqrt(x)/2]
#2
the term
Inc-t/bc
makes no sense to me, put in the needed brackets