Question

Log0. 5(2x-4)<log0.5(x+1)​

Answer 1

$\log_{0,5}(2x-4)x+1\\x>5$

Меняем знак неравенства, т.к. основание логарифма меньше 1.

Answer 2

To solve the inequality log₀.₅(2x - 4) < log₀.₅(x + 1), we need to apply the properties of logarithms to simplify the expression.

First, recall the property of logarithms: logᵦ(a) < logᵦ(b) if and only if a < b, where a, b, and β (the base) are positive real numbers.

Step 1: Rewrite the inequality using the property of logarithms.

log₀.₅(2x - 4) < log₀.₅(x + 1)

Step 2: Since the base of the logarithm is the same (0.5 in this case), we can drop the logarithm and just compare the expressions inside.

2x - 4 < x + 1

Step 3: Now, solve for x.

2x - x < 1 + 4

x < 5

So, the solution to the inequality is x < 5.