Answer:
Option b
Step-by-step explanation:
According to the property of sum of logarithms we know that
[tex]log(ab) = log(a) + log(b)[/tex].
In this case we have the equation:
[tex]log(2x) = 3[/tex]
Using the property of sum of logarithms:
[tex]log(2) + log(x) = 3[/tex]
[tex]log(x) = 3 - log(2)[/tex]
We also know that:
[tex]10 ^{(logx)} = x[/tex] -------- Inverse logarithm
So:
[tex]x = 10 ^{3-log(2)}[/tex]
[tex]x = 500[/tex]
Another easiest way to solve it is the following:
Make [tex]w = 2x[/tex].
Then:
[tex]log(2x) = log(w)[/tex]
[tex]log(w) = 3[/tex]
[tex]w = 10^3[/tex] -------- Inverse logarithm property
[tex]w = 1000[/tex]
but [tex]w= 2x[/tex]. Then:
[tex]2x = 1000\\\\x = 500[/tex]
