Question

What is the solution to the equation log 2 x – log 2 4 = 2 ?

Answer 1

log a - log b = log( a/b)

Answer 2

Use that property first and then put the equation into its exponential form.

Answer 3

so we have:
\[\log_{2} x - \log_{2} 4=2\]
Applying the property mertsj said, we'll end up with:
\[\log_{2} \frac{ x }{ 4 }=2\]
Now, we have to get rid of that logaritm so we'll transform the 2 on the right side of the equality to a logaritm that we know is true:
\[\log_{2} 4= 2 \]
so let's replace it:
\[\log_{2} \frac{ x }{ 4 }=\log_{2} 4\]
So now that we have Log2 on both sides, we can work like a very basic algebraic equation:
\[\frac{ x }{ 4 }=4\]
I encourage you to solve for x here and on :)

Answer 4

x=16?

Answer 5

Good, now to verify the value, replace 16 on the x of the orignal equation.