Question

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

Answer 1

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)`

`= log32/log2 + log_2(x + 2)(x - 2)`

`= (log2^5)/log2 + 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)`

Hopefully this helps!