Logarithms

Question

First question:  use the properties of logarithms to rewrite each expression as a single logarithm 

1) log x + log(8)

2) 3 log x + log y 

Second question: 

Expand each of the following in terms of simpler logarithms. Assume that all variable expressions are positive real numbers 

1)log[5x(y⁷)]

Answer 1

(1)

 

logx + log8 = log(8x)

 

(2)

 

3 logx + logy = log(x³) + logy = log(x³y)

 

(3)

 

log(5xy⁷) = log5 + logx + 7 logy