Question

2 log2 8 + log2 25\16 -  log2 25

Answer 1

2*log2_2^3 + log2_ (25/16 :25)=2*3 +log2_(1/16)=6-4=2

Answer 2

To simplify the given expression, let's use logarithmic properties:

1. log base b (x^n) = n * log base b (x)
2. log base b (x * y) = log base b (x) + log base b (y)
3. log base b (x / y) = log base b (x) - log base b (y)

Using these properties, we can simplify the expression:

2 log2 8 + log2 (25/16) - log2 25

First, let's simplify each term individually:

1. log2 8 = log2 (2^3) = 3 log2 2 = 3 (since log base b (b) = 1)

2. log2 (25/16) = log2 25 - log2 16 = log2 (5^2) - log2 (2^4) = 2 log2 5 - 4 log2 2 = 2 log2 5 - 4

3. log2 25 = log2 (5^2) = 2 log2 5

Now we substitute these values back into the expression:

2 log2 8 + log2 (25/16) - log2 25 = 2(3) + (2 log2 5 - 4) - 2 log2 5 = 6 + 2 log2 5 - 4 - 2 log2 5 = 2

Therefore, the simplified expression is 2.