Evaluate the expression.?

0 ⤊

Evaluate the expression.?

log2(112)-log2(7)

2006-12-03 12:33:32 · 3 answers · asked by im_all_about_spades2003 1 in Science & Mathematics ➔ Mathematics

3 answers

log2(112)-log2(7)
= log2 (112/7)
= log2 (16)

which means 2 to the what power is 16

so 4

2006-12-03 12:38:45 · answer #1 · answered by hayharbr 7 · 0⤊ 0⤋

This is a cute one, because the easiest way to do it without a calculator is to note that:

log2(x)-log2(y) = log2(x/y)

In this case, x/y = 112/7 = 16

So log2(112) - log2(7) = log2(16) = 4

That's because log2(anything) is the power you need to raise 2 to to get that number, and 2^4 = 16

2006-12-03 20:36:54 · answer #2 · answered by firefly 6 · 0⤊ 0⤋

note 112 = 7(16) = 7(2^4)

log2(112) -log2 (7) = log2(112/7) = log2(16*7/7) = log2(16) = 4

2006-12-03 20:37:14 · answer #3 · answered by Dennis T 1 · 0⤊ 0⤋