Question

Log 17 (x+10) < log 17 ( 1+√5+x)?? срочно!! помогите пожалуйста​

Answer 1

Ответ:в прикреплённом файле

Пошаговое объяснение:

Answer 2

Problem Statement

You are looking for a detailed explanation of the inequality log 17 (x + 10) < log 17 (1 + √5 + x).

Solution

To solve the given inequality, we need to understand the properties of logarithms and apply them to simplify the expression.

Logarithmic Properties

1. Product Rule: log base b (xy) = log base b (x) + log base b (y) 2. Quotient Rule: log base b (x/y) = log base b (x) - log base b (y) 3. Power Rule: log base b (x^a) = a * log base b (x)

Applying the Logarithmic Properties

Let's start by applying the quotient rule to the given inequality:

log 17 (x + 10) < log 17 (1 + √5 + x)

Using the quotient rule, we can rewrite the inequality as:

log 17 [(x + 10) / (1 + √5 + x)] < 0

Next, let's simplify the expression inside the logarithm:

[(x + 10) / (1 + √5 + x)]

Simplifying further, we can cancel out the common term 'x' in the numerator and denominator:

[(10) / (1 + √5)]

Now, let's rewrite the inequality with the simplified expression:

log 17 [(10) / (1 + √5)] < 0