Use properties of logarithms to condense the logarithms expression.

Question

Use properties of logarithms to condense the logarithms expression. write the expression as a single logarithm whose coefficient is 1. where possible, evaluate logarithmic expression.

 

1/2(log ₅x + log ₅y) -4 log ₅(x+6)  

 

Answer 1

Hello Cathryn -

 

A log of the product is the sum of the logs, as logs follow the rules of exponents. So the first term becomes log₅ (xy)^1/2.

 

The second term is then log₅(x+6)⁴. 

 

The difference of logs implies division, so what is the answer? I'll leave that to you.

 

Hope this helps,

 

Ken