How do you find ${log}_{2} [32 (x^{2} - 4)]$ $\log _ { 2} [ 32( x ^ { 2} - 4) ]$ ?

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How do you find ${log}_{2} [32 (x^{2} - 4)]$ $\log _ { 2} [ 32( x ^ { 2} - 4) ]$ ?

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Answer 1 · 2016-12-13T14:39:15

For problems like these, we expand the logarithms using the sum and difference rules and evaluate if possible.

$= {log}_{2} (32) + {log}_{2} (x^{2} - 4)$ $=log_2(32) + log_2(x^2 - 4)$

$= \frac{log 32}{log 2} + {log}_{2} (x + 2) (x - 2)$ $= log32/log2 + log_2(x + 2)(x - 2)$

$= \frac{{log 2}^{5}}{log 2} + {log}_{2} (x + 2) + {log}_{2} (x - 2)$ $= (log2^5)/log2 + log_2(x + 2) + log_2(x - 2)$

$= \frac{5 log 2}{log 2} + {log}_{2} (x + 2) + {log}_{2} (x - 2)$ $= (5log2)/log2 + log_2 (x + 2) + log_2 (x - 2)$

$= 5 + {log}_{2} (x + 2) + {log}_{2} (x - 2)$ $=5 + log_2 (x +2) + log_2 (x- 2)$

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How do you find ${log}_{2} [32 (x^{2} - 4)]$ $\log _ { 2} [ 32( x ^ { 2} - 4) ]$ ?

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How do you find ${log}_{2} [32 (x^{2} - 4)]$ $\log _ { 2} [ 32( x ^ { 2} - 4) ]$ ?