Thread: Laws of logarithms

I am familiar with the laws of logarithms, and there are three exam questions here that are each worth three marks:

1] Show that if x > 0,


2] Given that x > 0, y > 0, show that


3] Given that x > 0, y > 0, show that


How would you prove these laws? Would you show how you reach them or possibly use an example to do this?

Hello db5vry

Originally Posted by db5vry

I am familiar with the laws of logarithms, and there are three exam questions here that are each worth three marks:

1] Show that if x > 0,


2] Given that x > 0, y > 0, show that


3] Given that x > 0, y > 0, show that


How would you prove these laws? Would you show how you reach them or possibly use an example to do this?

I think that you are expected to prove each of these by using the definition of a logarithm, which is:

'The log of a number to a given base is that power to which the base must be raised to give the number'

In other words,

So you'd do number 1, for instance, like this:











Do you want to have a go at the others in the same way?

Grandad