Use the Laws of Logarithms to expand the expression (a and b), or combine the expression (c and d)

Question

a) log (a² / b⁴ √c)

 

b) ln (√x² +4 / (x² + 1)(x³ - 7)²)
c) 4 ln x −1/3 ln(x² + 1) + 2 ln(x − 1)

d) log 5 + 2 log x + 3 log(x² + 5)

Answer 1

Use these properties.

 

 

Addition:

 

log(xy) = log(x) + log(y)

 

 

Division:

 

log(x / y) = log(x) - log(y)

 

 

Exponents:

 

log(x^a) = alog(x)

 

 

Combine these properties to expand each expression.  The same applies to natural logs (Ln) too.