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Rewrite expression using properties of logarithms. `log_(b)((x^(3)sqrt(y))/(z+1)^(4))`  

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user354582 | Honors

Posted June 18, 2013 at 4:46 AM via web

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Rewrite expression using properties of logarithms.

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

 

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llltkl | College Teacher | Valedictorian

Posted June 18, 2013 at 5:27 AM (Answer #1)

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`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)`

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