Question

Решите неравенство: log 0.7 x < 1

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the inequality $\log_{0.7} x < 1$, we need to rewrite it in a way that isolates the logarithmic term and then solve for $x$. Here's how to do it step by step:

Step 1: Recall the logarithmic property $\log_a b < c$ is equivalent to $b < a^c$. Using this property, we can rewrite the given inequality as:

$0.7^{\log_{0.7} x} < 0.7^1$

Step 2: Since $0.7^1 = 0.7$, we have:

$0.7^{\log_{0.7} x} < 0.7$

Step 3: Now, we can remove the base and rewrite the inequality as:

$x < 0.7$

So the solution to the inequality is $x$ being any real number less than $0.7$, in interval notation: $x \in (-\infty, 0.7)$.