Question

Simplify:
A) log(x+1)+3logx

B) 2log4np-3log4p

C) 2ln(3x)+ln(5x)-ln6xy

D) 22log10+log1000-log1

Answer 1

D) 2log10+log1000-log1

Answer 2

A)
log(x+1)+3logx
log(x+1)+log(x^3)
log (x+1)(x^3)
log(x^4+x^3)

B)
2log(np)-3log(p)
log((np)^2)-log(p^3)
log(n^2p^2)-log(p^3)
log(n^2p^2/p^3)
log(n^2/p)
the base 4 is not important. These steps hold regardless of the base.

If the base is not 4, but the 4 is included in the expression, then the final log is
log(n^2/4p)

C)
2ln(3x)+ln(5x)-ln(6xy)
ln(9x^2*5x/6xy)
ln(15x^2 / 2y)

D)
2log10+log1000-log1
log100+log1000-log1
2+3-0
5