How do you expand this logarithm?

#log_(3)(z^(4)sqrtx)#

2 Answers
Alan P.
Nov 21, 2016

#4log_3 (z) + 1/2log_3(x)#

Explanation:

General Rules:
#color(white)("XXX")log_b a^c = c * log_b a#

#color(white)("XXX")log_b (a * c) = log_b + log_b c#

Geoff K.
Nov 21, 2016

#4log_3(z)+1/2log_3(x)#.

Explanation:

By using the rule of logarithms where #log(a*b)=loga+logb#, we first get

#log_3(z^4sqrtx)#
#=log_3(z^4)+log_3(sqrtx)#
#=log_3(z^4)+log_3(x^(1//2))#

Another rule of logarithms is #log(a^b)=blog(a)#. We now use this to get

#=4log_3(z)+1/2log_3(x)#

Unless you have been asked to rewrite the "base 3" logarithms in "base 10" form, this is as much expansion as we can do.

Hope this helps!

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