Expand the following as much as possible using the properties of logarithms. Express exponents and radicals as a) log⁡(xy3z2) b) ln⁡(x1−x3)

Question

Sadie Eaton · Accepted Answer

Step 1 (11) We know that, from the property of logarithm log⁡(mn)=log⁡(m)−log⁡(n)……(1) log⁡(mn)=log⁡(m)+log⁡(n)……(2) log⁡(a)b=blog⁡(a)……(3) (a) We have the given logarithmic expression as log⁡(xy3z2) On using the property of logarithm given by equation (1), (2) and (3), we get the result as log⁡(xy3z2)=log⁡(xy3}−log⁡(z)2 =log⁡[(x)12(y)32]−log⁡(z)2 =log⁡(x)12+log⁡(y)32−2log⁡(z)2 =12log⁡(x)+32log⁡(y)−2log⁡(z) Hence, value of the term log⁡(xy3z2) is 12log⁡(x)+32log⁡(y)−2log⁡(z) Step 2 (b) We have the given logarithmic expression as log⁡(x1−x3) On using the property of logarithm given by equation (1), (2) and (3), we get the result as log⁡(x1−x3)=log⁡(x)−log⁡(1−x3 =log⁡(x)−log⁡(1−x)13 =log⁡(x)−13log⁡(1−x) Hence, value of the term log⁡(x1−x3) is log⁡(x)−13log⁡(1−x)

Expand the following as much as possible using the properties of logarithms. Express exponents and radicals as\log (\frac{\sqrt{xy^{3}}}{z^{2}})

Answered question

Answer & Explanation

New Questions in Pre-Algebra