How do you use the properties of logarithms to rewrite(contract) each logarithmic expression #2log_2(64) + log_2(2)#?

1 Answer
George C.
Jul 19, 2015

Use #log_a(a^b) = b# to find:

#2log_2(64)+log_2(2) = 2*6+1 = 13#

Explanation:

#log_a(a^b) = b#, so

#64=2^6# so #log_2(64) = log_2(2^6) = 6#

#2=2^1# so #log_2(2) = log_2(2^1) = 1#

So #2log_2(64)+log_2(2) = 2*6+1 = 13#

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