Question

Log5(4x-3)>log5(3-2x)

Answer 1

Ответ:

решение на фотографии

Answer 2

To solve the inequality log5(4x - 3) > log5(3 - 2x), you can use the properties of logarithms.

First, remember that if you have log base a of x greater than log base a of y, then x must be greater than y.

So, in your case:

log5(4x - 3) > log5(3 - 2x)

This implies that:

4x - 3 > 3 - 2x

Now, you can solve for x:

Add 2x to both sides:

4x + 2x - 3 > 3

Combine like terms:

6x - 3 > 3

Add 3 to both sides:

6x - 3 + 3 > 3 + 3

6x > 6

Now, divide by 6 (which is a positive number, so the inequality direction doesn't change):

(6x) / 6 > 6 / 6

x > 1

So, the solution to the inequality log5(4x - 3) > log5(3 - 2x) is:

x > 1