Rewrite expression using properties of logarithms.

`log_(b)((x^(3)sqrt(y))/(z+1)^(4))`

### 1 Answer | Add Yours

`log_(b)[(x^3sqrty)/((z+1)^4)]`

Expressing radical in the form of exponent we get` log_b[(x^3*y^(1/2))/(z+1)^4]`

using the quotient property `log_b(x/y)=log_b(x)-log_b(y)`

`=log_b(x^3*y^(1/2))-log_b(z+1)^4`

using the product property `log_b(xy)=log_b(x)+log_b(y)`

`=log_bx^3+log_by^(1/2)-log_b(z+1)^4`

using the exponent property `log_b(x)^d=dlog_b(x)`

`=3log_bx+1/2log_by-4log_b(z+1)`

**Hence**, `log_(b)[(x^3sqrty)/((z+1)^4)]` `=3log_bx+1/2log_by-4log_b(z+1)`

**Sources:**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes