Question

Ex c)
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Answer 1

$\it C = 4(log_2x^3)^2 + 2log_2(8x^{-6})-(1-6log_2x)^2$

$\it 4(log_2x^3)^2 =2^2(log_2x^3)^2 = (2log_2x^3)^2 =(log_2x^6)^2 \ \ \ \ (1)$

$\it 2log_2(8x^{-6})=2(log_28+log_2x^{-6})=2(log_2 2^3 +log_2(x^6)^{-1})=\\\\2[3+(-1)log_2x^6]=6-2log_2x^6 \ \ \ \ (2)$

$\it (1-6log_2x)^2=(1-log_2x^6)^2 = 1-2log_2x^6+(log_2x^6)^2\ \ \ \ (3)$

$\it (1),(2),(3) \Rightarrow C = (log_2x^6)^2+6-2log_2x^6-1+2log_2x^6-(log_2x^6)^2=5$