Question

Lg(x-5)<=1 Решите неравенство

Answer 1

$\lg(x-5)\leq1\\O.D.3.:\;x-5>0\Rightarrow x>5\\\\x-5\leq10^1\\x-5\leq10\\x\leq15\\\\OTBET:\;(5;\;15]$

Answer 2

Ответ:    $x\in (5,15\, ]$

Пошаговое объяснение:

$lg(x-5)\leq 1\; \; ,\; \; ODZ:\; x>5\\\\lg(x-5)\leq lg10\\\\x-5\leq 10\\\\x\leq 15\\\\\underline {x\in (5,15\, ]}$

Answer 3

To solve the inequality $lg(x-5) \leq 1$, we need to find the values of $x$ that satisfy the inequality. In this context, "lg" usually refers to the logarithm with base 10, commonly denoted as $\log_{10}$. The inequality can be rewritten as:

$\log_{10}(x-5) \leq 1$

To remove the logarithm, we can rewrite the inequality in exponential form:

$10^{\log_{10}(x-5)} \leq 10^1$

Remember that $10^1 = 10$, so we have:

$x - 5 \leq 10$

Now, let's solve for $x$:

$x \leq 10 + 5$

$x \leq 15$

So the solution to the inequality is $x \leq 15$. In interval notation, it can be written as $(- \infty, 15]$, meaning all real numbers less than or equal to 15 satisfy the original inequality.