Question

Expand each expression

Ln 4y^5/x^2 ?


A = In 4 - 2 In x - 5 In y

B = In 4 - 2 In x + 5 In y

C = -8 In x + 5 In y

Answer 1

the answer is B

Explanation:

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Answer 2

Option B -
`\ln((4y^5)/(x^2))=\ln 4+5\ln y-2\ln x`

Explanation:

Given : Expression
`\ln((4y^5)/(x^2))`

To find : Expand each expression ?

Solution :

Using logarithmic properties,

`\ln ((A)/(B))=(\ln A)/(\ln B)=\ln A-\ln B`

and
`\ln (AB)=\ln A+\ln B`

Here, A=4y^5 and B=x^2

`\ln((4y^5)/(x^2))=(\ln 4y^5)/(\ln x^2)`

`\ln((4y^5)/(x^2))=\ln 4y^5-\ln x^2`

`\ln((4y^5)/(x^2))=\ln 4+\ln y^5-\ln x^2`

Using logarithmic property,
`\logx^a=a\log x`

`\ln((4y^5)/(x^2))=\ln 4+5\ln y-2\ln x`

Therefore, option B is correct.