# How do you solve log2+logx=1?

Jul 12, 2016

5 (Assuming $\log = {\log}_{10}$)

#### Explanation:

${\log}_{10} 2 + {\log}_{10} x = 1$

Using: ${\log}_{n} a + {\log}_{n} b = {\log}_{n} \left(a b\right)$ we may rewrite the equation as:

${\log}_{10} 2 x = 1$

Using: ${\log}_{n} a = b \to a = {n}^{b}$ we may simplify the equation as:

$2 x = {10}^{1}$

$2 x = 10$

$x = 5$