Question

Log2 6+log2 3- log2 36

Answer 1

Ответ:  -1

Пошаговое объяснение:

= log2 6+log2 3-2log2 6=log2 3 -log2 6=log2 3-log2 (2*3)=log2 3-log2 2-

log2 3=-1

Answer 2

To simplify the expression $\log_2 6 + \log_2 3 - \log_2 36$, you can use logarithmic properties to combine and simplify the terms.

1. First, recall the logarithmic property $\log_b M + \log_b N = \log_b (M * N)$. This means that when you add two logarithms with the same base, you can multiply the numbers inside the logarithms.

2. Similarly, $\log_b M - \log_b N = \log_b (M / N)$. When you subtract two logarithms with the same base, you can divide the numbers inside the logarithms.

Let's apply these properties to your expression:

$\log_2 6 + \log_2 3 - \log_2 36$

Using the addition property for the first two terms:

$\log_2 (6 * 3) - \log_2 36$

Now, simplify inside the logarithms:

$\log_2 (18) - \log_2 36$

Now, using the subtraction property:

$\log_2 (18 / 36)$

Further simplify inside the logarithm:

$\log_2 (1/2)$

Now, $\log_2 (1/2)$ represents the exponent to which 2 must be raised to equal 1/2. Since $2^{-1} = 1/2$, we can rewrite it as:

$\log_2 (2^{-1})$

And by the logarithmic property, $\log_b (b^n) = n$, we get:

$-1$

So, $\log_2 6 + \log_2 3 - \log_2 36 = -1$.