# How do you solve 2log_2 (x )+ log_2 (1)= log_2 (4)?

Dec 24, 2015

Step by step explanation is given below.

#### Explanation:

$2 {\log}_{2} \left(x\right) + {\log}_{2} \left(1\right) = {\log}_{2} \left(4\right)$

Let us use rules of logarithms

$1. {\log}_{b} \left(1\right) = 0$ $\log \left(1\right)$ to any base is zero
$2. {\log}_{b} \left({a}^{n}\right) = n {\log}_{b} \left(a\right)$
$3. {\log}_{b} \left(A\right) = {\log}_{b} \left(C\right) \implies A = C$

$2 {\log}_{2} \left(x\right) + 0 = {\log}_{2} \left({2}^{2}\right)$ by rule 1 and rewriting 4 as 2^2

$2 {\log}_{2} \left(x\right) = 2 {\log}_{2} \left(2\right)$ by rule 2
${\log}_{2} \left(x\right) = {\log}_{2} \left(2\right)$ After dividing by 2 on both sides.
$x = 2$ by rule 3.

The solution is $x = 2$