Question

How do you expand `(ln(5^1))(ln(2/(3^-2)^-2)`?

Answer 1

`ln(5)(ln(2)-4ln(3))`

Explanation:

Begin by simplifying the second factor. We can distribute the negative exponent in the denominator as such:

`ln(5^1)ln(2/(3^-2)^-2)=ln(5)ln(2/3^4)`

Next we can use the quotient property of logarithms to expand the second term:

`ln(5)ln(2/3^4) = ln(5)(ln(2)-ln(3^4))`

Finally, we can use the power property logarithms to move the negative exponent outside the logarithm:

`ln(5)(ln(2)-ln(3^4)) = ln(5)(ln(2)-4ln(3))`