Question

Select the correct answer.

How would you write this expression as a sum or difference?


`log_(3) (^(5√(x)) X y )`

Answer 1

`\log_(3) ({5√(x)} * y ) = \log_(3)({5) + \log_(3)(√(x)) +\log_(3)( y )`

Explanation:

Given

`\log_(3) ({5√(x)} * y )`

Required

Write as sum or difference

Using addition law of logarithm, the equation becomes:

`\log_(3) ({5√(x)} * y ) = \log_(3)({5√(x)) +\log_(3)( y )`

Expand

`\log_(3) ({5√(x)} * y ) = \log_(3)({5 * √(x)) +\log_(3)( y )`

Apply addition law

`\log_(3) ({5√(x)} * y ) = \log_(3)({5) + \log_(3)(√(x)) +\log_(3)( y )`