How do you simplify $log 100^x$ ?

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Answer 1 · 2016-07-11T23:59:24

Recall the log rule that states $loga^n = nloga$ :

$log100^x = xlog100 = x(log100)$

Now, remember the change of base rule $log_a(n) = log(n)/log(a)$ . In this case, $a = 10$ .

$=x(log100/log10)$

$=x(log10^2/log10^1)$

$=x((2log10)/(1log10))$

$= x(2)$

$= 2x$

Hopefully this helps!

How do you simplify log 100^xlog 100^x?