Question

homework3: problem 1 (2 points)
evaluate the following expression. (note: your answer cannot contain a logarithm)
$4\log_4(256)-2\log_4(64)=\square$
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Explanation:

Step1: Recall log - property $a\log_b(x)=\log_b(x^a)$

$4\log_4(256)-2\log_4(64)=\log_4(256^4)-\log_4(64^2)$

Step2: Simplify the arguments

Since $256 = 4^4$ and $64 = 4^3$, then $256^4=(4^4)^4 = 4^{16}$ and $64^2=(4^3)^2=4^6$. So the expression becomes $\log_4(4^{16})-\log_4(4^6)$.

Step3: Recall log - property $\log_b(b^x)=x$

$\log_4(4^{16}) = 16$ and $\log_4(4^6)=6$.

Step4: Calculate the result

$16 - 6=10$

Answer:

$10$