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

1 Answer
Kevin G.
Dec 15, 2015

#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))#

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