Using the properties of logarithims to write the expression as a single logarithim, if possible:

Question

2loga 5x^3-1/2loga(2x+3)

Answer 1

The quotient rule of logarithms means that loga x - loga y = loga (x/y). So we need to convert this to a quotient.

2loga 5x^3=loga 5x^6

1/2loga(2x+3)=loga (2x+3)^.5

2loga 5x^3-1/2loga(2x+3)=loga 5x^6-loga (2x+3)^.5=loga(5x^6)/(2x+3)^.5

 

Hope that helps,

Deanna