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

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Answer 1 · 2015-07-19T12:59:13

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

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

$log_a(a^b) = b$ , 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 $2log_2(64)+log_2(2) = 2*6+1 = 13$

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