SOLUTION: i need help in expanding {{{ log(2,((32) root(3,x))/(y^3)) }}}as much as possible

Question 374976: i need help in expanding as much as possible
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!

For this we will need all three properties of logarithms:

Since the argument of our initial logarithm is a fraction/division we will use the second property to split the numerator and denominator into separate logarithms:

This argument of the first logarithm is a product so we can use the first property to split the factors into separate logarithms:

Since 1/3 as an exponent means the same thing as a cube root, I am going to replace the cube root with an exponent of 1/3:

Now we can use the third property on the two logarithms with exponents on their arguments. (This is why I changed the cube root into a power of 1/3.)

Last of all, since the first logarithm simplifies to 5:

This, I believe, is the desired answer.
RELATED QUESTIONS
i need help solving this equation {{{ log(2,x)+log(2,x-6)=4 }}} and finding the domain... (answered by solver91311)

I need some help on these problems. 1. y varies directly as x and inversely as the... (answered by stanbon,jim_thompson5910)

Write as a single logarithm {{{3logx-(1/2)log(x-2)+2log(x+5)^3}}} PLZ help I need tis... (answered by stanbon,jim_thompson5910)

Im not sure how to write the expression as the logarithm of a single quantity...... (answered by longjonsilver,rapaljer)

I need help writing 1/2 log(25) - 3 log(x) as a single... (answered by asuar010)

Hi, I really really need to submit my math homeworks as soon as possible, but I cant... (answered by Edwin McCravy)

Write as a single logarithm a) 2 log 5 log b b) 3 log x + 1/2 log y c) 2 log m + log n (answered by lwsshak3)

I need help in writing the expression as one logarithm: 2 log (Y^10/x) - 6 log y + 1/2 (answered by lwsshak3)

Multiply: (2y-1)(y+3) Multiply: (z^2-4z+4)(z-2) Need help as soon as possible thank (answered by ewatrrr)