Question

Уравнение:3^(х+1)+18×3^-х=29

Answer 1

См. решение здесь....

Answer 2

I can help you solve this equation. First, let's rewrite it using the same base for both terms:

$$3^{x+1} + 18 \times 3^{-x} = 29$$

$$3^{x+1} + \frac{18}{3^x} = 29$$

$$\frac{3^{x+1} \times 3^x}{3^x} + \frac{18}{3^x} = 29$$

$$\frac{3^{2x+1} + 18}{3^x} = 29$$

Next, let's multiply both sides by $3^x$ and simplify:

$$3^{2x+1} + 18 = 29 \times 3^x$$

$$3^{2x+1} - 29 \times 3^x + 18 = 0$$

Now, we have a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 3$, $b = -29$, and $c = 18$. We can use the quadratic formula to find the value of $x$:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

$$x = \frac{29 \pm \sqrt{(-29)^2 - 4 \times 3 \times 18}}{2 \times 3}$$

$$x = \frac{29 \pm \sqrt{529 - 216}}{6}$$

$$x = \frac{29 \pm \sqrt{313}}{6}$$

Since $x$ is an exponent, we only consider the positive root:

$$x = \frac{29 + \sqrt{313}}{6}$$

This is the exact solution. If you want an approximate value, you can use a calculator to get:

$$x \approx 1.527$$

I hope this helps you understand how to solve this equation. If you have any other questions, feel free to ask me.Ответь+подробно.+Уравнение:3^(х+1)+18×3^-х=29