Question

Log2 (x-5)<1|-3-2x|=13-5i/5-3i

Answer 1

Решила только два задания.

Answer 2

To solve the equation involving logarithm and absolute value, you'll need to consider two cases based on the absolute value expression. Let's solve it step by step:

Case 1: 3 - 2x ≥ 0 (when the absolute value is positive) In this case, you don't need to worry about the absolute value, so the equation becomes:

Log₂(x - 5) < 1 - |3 - 2x| = 1 - (3 - 2x)

Simplify:

Log₂(x - 5) < 2x - 2

Now, rewrite the inequality:

x - 5 < 2^(2x - 2)

Case 2: 3 - 2x < 0 (when the absolute value is negative) When the absolute value is negative, we flip the sign:

Log₂(x - 5) < 1 + |3 - 2x| = 1 + (2x - 3)

Simplify:

Log₂(x - 5) < 2x - 2

Now, rewrite the inequality:

x - 5 < 2^(2x - 2)

Now, we have two inequalities:

1. x - 5 < 2^(2x - 2)
2. x - 5 > 2^(2x - 2)

Let's solve each of them separately:

Solving Inequality 1: x - 5 < 2^(2x - 2)

First, move 2^(2x - 2) to the left side:

x - 2^(2x - 2) - 5 < 0

To simplify further, we can use a substitution. Let's set y = 2x - 2:

x - 2^y - 5 < 0

Now, rewrite the inequality in terms of y:

x - 2^y - 5 < 0

To solve for y, you may need to use numerical methods or graphing software because this is a transcendental equation, which doesn't have a simple algebraic solution.

Solving Inequality 2: x - 5 > 2^(2x - 2)

Similarly, move 2^(2x - 2) to the right side:

x - 5 > 2^(2x - 2)

Again, set y = 2x - 2:

x - 2^y - 5 > 0

This inequality is also transcendental and may require numerical methods or graphing software to find the solution.

Without knowing the specific value of x or using numerical methods, we can't provide exact solutions to these inequalities. You would need to use a numerical solver or graphing techniques to find approximate solutions for both inequalities.