🧮 algebra

1. **Problem Statement:** Find the number of real-valued solutions to the equation $$2^x + 2^{-x} = 2 - (x-2)^2.$$\n\n2. **Rewrite the equation:** Let us analyze the left side firs

1. **State the problem:** Solve for $2^x$ given the equation $4^x = 32^{x-3}$. 2. **Rewrite bases as powers of 2:**

1. The problem asks to solve or analyze parts 27)c, 27)e, and 27)h from a given set, but since only the first question must be solved, we focus on 27)c. 2. Without the original pro

1. **Problem:** Consider the equation $$2x^2 + 4y^2 + 8x - 16y + F = 0$$. Find all values of $$F$$ such that the graph of the equation a. is an ellipse

1. Diberikan persamaan: $$^4\log^2 x - 3(^4\log x) + 2 = 0$$. 2. Misalkan $$y = ^4\log x$$, sehingga persamaan menjadi: $$y^2 - 3y + 2 = 0$$.

1. **State the problem:** Solve the equation $$^m\log(2x + 6) \cdot ^5\log m = 2$$ for $x$. 2. **Recall the change of base formula:** For any positive numbers $a,b,c$ with $a \neq

1. Let's start with a fun activity to understand GEMDAS, which stands for Grouping symbols, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (f

1. The problem is to understand what the non-associativity of octonions means. 2. Octonions are an extension of complex numbers and quaternions, forming an 8-dimensional algebra ov

1. **State the problem:** Multiply and simplify the expression $$\frac{9m^2 n}{12m n^4} \times \frac{16m^3 n^2}{6m^2}$$. 2. **Write the multiplication of fractions:**

1. **State the problem:** Simplify the expression $$\frac{2x^2 + 9x + 4}{x + 4}$$. 2. **Recall the formula:** To simplify a rational expression, factor the numerator and denominato

1. The problem is to perform long division of polynomials or numbers and show the steps clearly. 2. Long division is a method to divide one number or polynomial (dividend) by anoth

1. **State the problem:** Simplify the expression $\frac{18x}{6x}$. 2. **Recall the rule:** When dividing fractions or terms, divide the numerators and denominators separately. Als

1. **State the problem:** Simplify the expression $$\frac{48a^3 b^2}{18a b^5}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{48a^3 b^2}{18a b^5}$$. 2. **Write the formula and rules:** When simplifying fractions with variables, divide coefficients

1. **State the problem:** Solve the system of linear equations: $$x - 2y = 2$$

1. **State the problem:** We need to find the value of $f(-2 - g(3))$ given the functions $f(x) = \frac{3}{4}x + 10$ and $g(x) = x^2 - 3$. 2. **Calculate $g(3)$:** Substitute $x=3$

1. **State the problem:** Simplify the expression $\frac{18x}{6x}$. 2. **Recall the rule:** When dividing fractions or terms, divide the numerators and denominators separately. Als

1. The question asks if the problem involves cancellation. 2. Cancellation in math typically occurs when simplifying fractions by removing common factors from numerator and denomin

1. **Stating the problem:** Find the conjugate of the polynomial expression $3 + 4i$. 2. **Formula and explanation:** The conjugate of a complex number $a + bi$ is $a - bi$. This m

1. **Problem Statement:** Find the conjugate of the complex number $z = a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit. 2. **Formula:** The conjugate of

1. **State the problem:** Simplify the expression $\frac{18x}{6x}$. 2. **Recall the rule:** When simplifying fractions, divide numerator and denominator by their greatest common fa