How Do You Solve log_{2}8x^{2} When log_{2}x Equals p?

[thomas49th]

Homework Statement

Given that $$log_{2}x = p$$
a) Find $$log_{2}8x^{2}$$ in terms of p

The Attempt at a Solution

take the power outside the log

$$2log_{2}8x$$

but i can't see what to do next

Any suggestions

Thanks :)

 

[Doc Al]

I assume you mean:
$${log}_{2}(8x^{2})$$

First things first. How do logs work with products? log(ab) = ?? (In your example, a = 8 and b = x^2.)

 

[thomas49th]

$$log_{2}8x^{2}$$

$$log_{2}8 + 2log_{2}x$$

$$3 + 2p$$

Thanks :)

it was easy!

 

[Doc Al]

Now you've got it!