Question

Log2x>log2(3-x) решите неравенмтво

Answer 1

$></p> <p>x>0</p> <p>x<3</p> <p>x>3/2</p> <p><strong>Ответ: </strong><em>Хє(1,5; 3)</em></p> </div> <div class=$ 0 0

Answer 2

To solve the inequality log2(x) > log2(3 - x), we need to use logarithm properties to simplify it. Remember that for any positive base "b":

1. log_b(a) > log_b(c) if and only if "a" is greater than "c" when both "a" and "c" are positive.

Let's use this property to solve the inequality step by step:

Step 1: Write the inequality in a simpler form by using the property mentioned above:

log2(x) > log2(3 - x)

Step 2: Set the expressions inside the logarithms as the bases to be equal:

2^log2(x) > 2^log2(3 - x)

Step 3: Use the fact that 2^log2(y) = y:

x > 3 - x

Step 4: Move "x" to one side of the inequality:

x + x > 3

2x > 3

Step 5: Divide both sides by 2:

x > 3/2

So the solution to the inequality is:

x > 3/2