Question

Determine if the following equations are equal by evaluating both sides

Log ((1-i)^3) = 3Log(1-i)

Answer 1

Yes, the both sides of the given equation are equal.

Explanation:

The given equation is

`\log((1-i)^3)=3\log(1-i)`

Taking LHS,

`LHS=\log((1-i)^3)`

Using the power property of logarithm, we get

`LHS=3\log(1-i)`
`[\because log_ax^n=nlog_ax]`

`LHS=RHS`
`[\because RHS=3\log(1-i)]`

Both sides of the given equation are equal.