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!