Question

Уравнение. 2^(5-3x)<1

Answer 1

$2 ^{5-3x}\ \textless \ 2^{0} \\ 5-3x\ \textless \ 0 \\ 3x\ \textgreater \ 5 \\ x\ \textgreater \ \frac{5}{3}$

x∈(5/3; +∞)

Answer 2

To solve the inequality 2^(5-3x) < 1, we can follow these steps:

Step 1: Rewrite 1 as a power of 2. 1 = 2^0

Step 2: Set the exponent expressions inside the inequality equal to each other. 5 - 3x = 0

Step 3: Solve the equation for x. 5 - 3x = 0 3x = 5 x = 5/3

Step 4: Analyze the intervals. Since we have the inequality 2^(5-3x) < 1, the exponent expression 5 - 3x must be negative for the inequality to hold. Since the base 2 is always positive, we can ignore it for determining the sign of the inequality.

For 5 - 3x to be negative, we need x > 5/3.

Step 5: Write the final solution. The solution to the inequality 2^(5-3x) < 1 is x > 5/3.