# Write the expression as a sum or difference of logarithms. Express powers as factors. Please show all of your work.Write the expression as a sum or difference of logarithms. Express powers as...

Write the expression as a sum or difference of logarithms. Express powers as factors. Please show all of your work.

Write the expression as a sum or difference of logarithms. Express powers as factors. Please show all of your work.

`log((7c^3)/d^8)`

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Expert Answers

hala718 | Certified Educator

`log ((7c^3)/d^8)`

`` First we will use the quotient properties:

`log (a/b) = log a - log b `

`=gt log (7c^3) - log d^8`

`` Now we will use the product property:

`==gt log ab = log a + log b `

`==gt log 7 + log c^3 - log d^8`

Now we will use the power property:

`==gt log a^b= blog a `

`==gt log 7 + 3log c - 8log d`