LOGARITHMIC PROPERTIES

Question

1) Expand the logarithmic expression log xy^2. *show your work*

2) Condense the logarithmic expression 1/2 log x - log y to a single logarithmic. *show your work*

Answer 1

the log of a product = the sum of the log of each factor of the product

logxy^2 = logx + logy^2

You can also convert the exponent to a coefficent, so logy^2 = 2logy

thus logxy^2 = logx + 2logy

(1/2)logx - logy = log(sqrx) - log y = log(sqrx/y)

Answer 2

1) log(xy^2) = log(x)+log(y^2) = log(x) + 2log(y)

2) 1/2 log(x) - log(y) = log(x^(1/2)) - log(y) = log( (x^(1/2))/y)