Write each expression as a sum andor difference of logs logx

Write each expression as a sum and/or difference of logs.

log(x^3(x+7)^5)

Solution

log(x^3(x+7)^5)

Since we are multiplying, we can rewrite using addition:

log x^3 + log (x+7)^5

Use the power rule to get:

3*log x + 5*log (x + 7)

This is the required expression of given logrithm.