🧮 algebra

1. Planteamos el problema: encontrar el valor de $n$ en la ecuación $$ (x^n) \log_x 3 = 3 \log_{\sqrt{3}} x + 2^{1 + 4 \log_x x} $$ 2. Recordemos algunas propiedades importantes de

1. Planteamos el problema: Resolver para $n$ la ecuación $$ (x^n) \log_x 3 = 3 \log_{\sqrt{3}} x + 2^{1+4 \log_x x} $$ 2. Recordemos algunas propiedades importantes de logaritmos y

1. **Compléter les pointilles :** - $(-158) \times 1 = -158$ car multiplier par 1 ne change pas le nombre.

1. مسأله: حل معادله $x^2 - 5x + 6 = 0$. 2. فرمول: معادله درجه دوم به شکل کلی $ax^2 + bx + c = 0$ است و ریشه‌ها با فرمول $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ محاسبه می‌شوند.

1. The problem is to simplify the square roots: $\sqrt{128}$, $\sqrt{192}$, $\sqrt{162}$, $\sqrt{243}$, $\sqrt{200}$, $\sqrt{500}$, $\sqrt{12}$, $\sqrt{18}$, $\sqrt{20}$, $\sqrt{45

1. The problem is to find the minimum natural number $n$ such that $f^n=0$, where $f^n$ denotes the $n$-th power of the function or operator $f$. 2. This is a problem about nilpote

1. The problem is unclear as stated: "Why sum xy i dalat. 75.3". It seems to ask about the sum of a product $xy$ or a related concept involving the number 75.3. 2. To clarify, if y

1. مسئله: جمع کردن دنباله اعداد $-2-4+6-8-10+12-\ldots-236-238+240$ است. 2. ابتدا دنباله را به صورت جفت جفت بررسی می‌کنیم: هر دو عدد اول را با هم جمع می‌کنیم، سپس دو عدد بعدی و همی

1. مسئله: محاسبه مجموع دنباله $$-2 - 4 + 6 - 8 - 10 + 12 - \ldots - 236 - 238 + 240$$ است. 2. ابتدا باید الگوی دنباله را شناسایی کنیم. دنباله شامل اعداد زوج از 2 تا 240 است که علام

1. مسئله: محاسبه مجموع دنباله اعداد 7 + 4 + 1 + ... + 85. 2. این دنباله یک دنباله حسابی است که هر جمله با کم کردن 3 از جمله قبلی به دست می‌آید.

1. **State the problem:** Solve for the variable $x$ in the equation $$\frac{1}{3} \times x = 9$$. 2. **Formula and rules:** To isolate $x$, multiply both sides of the equation by

1. **State the problem:** Solve for the variable $x$ in the equation $$\frac{1}{3}x = 9$$. 2. **Formula and rules:** To isolate $x$, multiply both sides of the equation by the reci

1. The problem asks whether the set of ordered pairs $\{(3,1), (4,1), (6,1), (8,1)\}$ is a function or a relation. 2. A relation is any set of ordered pairs.

1. **Énoncé du problème :** Soit la suite $(U_n)$ définie par $U_0 = 6$ et $U_{n+1} = \frac{U_n + 2}{5}$ pour tout $n \in \mathbb{N}$.

1. সমস্যাটি হলো: $m^2 - n^2 = 4\sqrt{mn}$ এবং $n = \tan\theta - \sin\theta$ দেওয়া আছে, $m$ এর মান নির্ণয় করতে হবে। 2. প্রথমে মূল সমীকরণটি লিখি:

1. **State the problem:** We want to analyze and understand the function $$y = \sqrt{3x^2 + 9}$$. 2. **Formula and rules:** The function involves a square root, so the expression i

1. **State the problem:** Simplify the expression $$\left(\frac{16}{81}\right)^{-\frac{3}{4}} \times \sqrt{\frac{100}{81}}.$$\n\n2. **Recall the rules:**\n- For any positive number

1. The problem is to plot the function $$f(x) = \left(\frac{1 + \sin x}{1 - \sin x}\right)^{\frac{1}{2}}$$ on the y-axis. 2. This function involves a square root of a fraction wher

1. **Problem statement:** Solve for $x$ in the equation $$e^{x-1} - 18e^{-x} - 3 = 0.$$ 2. **Rewrite the equation:** Recall that $e^{-x} = \frac{1}{e^x}$. So the equation becomes $

1. **State the problem:** Evaluate $$6. \left( \sqrt[6]{2^{12}} \right)^3$$. 2. **Recall the rules:** The sixth root of a number is the same as raising it to the power of $\frac{1}

1. Let's solve the first problem from 28.a: $5x + 9 - 4x^2 - 9 = 3.3$ 2. Simplify the equation by combining like terms: