Question

0,5log2 36-log2 3/2

Answer 1

log2(36)^1/2 - log2(3/2)= log2(6)-log2(3/2)= log2(6:3/2)= log2(4)= 2log2(2)= 2*1= 2

Answer 2

To simplify the expression 0.5log2(36) - log2(3/2), let's first evaluate each term separately and then perform the subtraction:

1. log2(36): We can simplify log2(36) by recognizing that 36 is a power of 2 (2^2 * 3^2 = 36). So, log2(36) = log2(2^2 * 3^2) = log2(2^2) + log2(3^2) = 2log2(2) + 2log2(3) = 2 + 2*log2(3).

2. log2(3/2): This can be simplified using the properties of logarithms. We know that log_b(a/b) = log_b(a) - log_b(b) = log_b(a) - 1. Applying this to our expression, log2(3/2) = log2(3) - log2(2).

Now, let's substitute the simplified forms back into the original expression:

0.5log2(36) - log2(3/2) = 0.5(2 + 2*log2(3)) - (log2(3) - log2(2)).

Now, distribute the 0.5: = 1 + log2(3) - (log2(3) - log2(2)).

Now, simplify further by canceling out log2(3): = 1 + log2(2).

Finally, the expression is simplified to: 1 + log2(2).

To get a numerical value for this expression, remember that log2(2) = 1, so:

1 + log2(2) = 1 + 1 = 2.