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

Question

mertsj · Answer

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

mertsj · Answer

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

owlcoffee · Answer

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 :)

anonymous · Answer

x=16?

owlcoffee · Answer

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