Core 5

Question 1

Prove that log(a)b=1/log(b) a

Answer 1

Let y= log(a) b so b=a^y
Take logs base b each side
Log(b) = logb (a^y)
1=ylog(b)a
1= log(a)b x log(b)a
So log(a)b=1/log(b)a

Question 2

Logs

Answer 2

Always reduce to 2 terms

Question 3

If asks for double

Answer 3

Take initial and double that

Then substitute into equation