Question

Log0,2(x+3)>log0,2 4

Answer 1

х+3>0

x>-3

x+3<4 (т.к основание логарифма меньше единицы, меняем знак)

х<4-3

x<1

ответ: (-3;1)

Answer 2

To solve the inequality log0.2(x+3) > log0.2(4), we need to first understand the properties of logarithms and apply them to simplify the expression.

The base of the logarithm is 0.2 in this case. We can rewrite the inequality as an exponent equation using the property that logb(x) = y is equivalent to bx = x.

Rewriting the given inequality, we have:

0.2^(log0.2(x+3)) > 0.2^(log0.2(4))

Simplifying further, we get:

(x + 3) > 4

Now, we solve for x by subtracting 3 from both sides of the inequality:

x > 4 - 3

x > 1

Therefore, the solution to the inequality log0.2(x+3) > log0.2(4) is x > 1.