# How do you solve log_2(2x)=log_2 100?

Jul 12, 2018

$\textcolor{b l u e}{x = 50}$

#### Explanation:

If:

${\log}_{a} \left(b\right) = {\log}_{a} \left(c\right) \implies b = c$

Hence:

${\log}_{2} \left(2 x\right) = {\log}_{2} \left(100\right)$

$2 x = 100 \implies x = \frac{100}{2} = 50$

Jul 12, 2018

$x = 50$

#### Explanation:

Since our bases are the same, we can essentially cancel them out and be left with

$2 x = 100$

By dividing both sides by $2$, this easily simplifies to

$x = 50$

Hope this helps!