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

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Answer 1 · 2016-06-12T13:34:58

$5 x = 100 \Rightarrow x = 20$ $5x = 100 " " rArr x = 20$

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.

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

$log x + log 5 = log 100 {log}_{10} 100 = 2$ $logx + log5 = log 100 " "log_10 100 =2$

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

$log 5 x = log 100$ $log 5x = log 100$

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

$5 x = 100 \Rightarrow x = 20$ $5x = 100 " " rArr x = 20$

How do you solve log x + log 5 = 2logx+log5=2log x + log 5 = 2?