Question

Log2(5x-9)>log2(3x+1)

Answer 1

Ответ:

Пошаговое объяснение:

5x-9>3x+1

2x>10

x>5

$x \in (5 ; \infty)$

Answer 2

To solve the inequality $\log_2(5x - 9) > \log_2(3x + 1)$, we can use the properties of logarithms.

Remember that if $a > b$, then $\log_a(c) > \log_b(c)$ for any positive value of $c$.

So, in your case, we have: $\log_2(5x - 9) > \log_2(3x + 1)$.

Using the property mentioned above, we can remove the logarithms: $5x - 9 > 3x + 1$.

Now, let's solve for $x$: $5x - 3x > 1 + 9$, $2x > 10$, $x > 5$.

So, the solution to the inequality is $x > 5$.