# Answer to Question #15487 in Algebra for Alisha

Question #15487

Simplify the following equations with rules of logarithms and exponents:

y = ln(ax^3)+b and y = ((x^4)+(3x^3))^7

y = ln(ax^3)+b and y = ((x^4)+(3x^3))^7

Expert's answer

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))

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))

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