Question

Simplify the following equations with rules of logarithms and exponents:
y = ln(ax^3)+b and y = ((x^4)+(3x^3))^7

Answer 1

ln(a*b)=lna+lnb also ln(a^x)=xlna, using these rules we've obtained 1.
second is (x^4+3x^3)^7=(x^3(x+3))^7=x^21(x+3)^7 (here we used that (ab)^c=(a^c)(b^c) and (a^b)^c=a^(bc))