Question

Решите неравенство: log5(2x)>2

Answer 1

log5 (2x)>2

log5 (2x)>2,x>0

2x>5^2

2x>25

x>25\2,x>0

x>25\2

Answer 2

To solve the inequality $\log_5(2x) > 2$, we need to isolate $x$ on one side of the inequality. Here's the step-by-step solution:

Step 1: Rewrite the inequality in exponential form: $\log_5(2x) > 2$ is equivalent to $5^2 < 2x$.

Step 2: Simplify the right side: $5^2 = 25$.

Step 3: Write the simplified inequality: $25 < 2x$.

Step 4: Divide both sides by 2 to solve for $x$: $\frac{25}{2} < x$.

The solution to the inequality is $x > \frac{25}{2}$, or $x > 12.5$.