# How do you solve log x + log 5 = 2?

Jun 12, 2016

$5 x = 100 \text{ } \Rightarrow x = 20$

#### Explanation:

Remember that with log questions, you can't work with log terms and number terms. Change them either all to log terms, or all to number terms.

$\log x + \log 5 = 2$ should rather be written as:

$\log x + \log 5 = \log 100 \text{ } {\log}_{10} 100 = 2$

Now apply the log law to get the log of a single term:
$\log x \times 5 = \log 100$

$\log 5 x = \log 100$

Because we have one log term on each side we can drop the logs and end up with

$5 x = 100 \text{ } \Rightarrow x = 20$