🧮 algebra

1. **Problem:** Use the properties of logarithms to expand the expression $3\ln a - \ln b + 5 \ln c$. 2. **Formula and rules:**

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. **Problem Statement:** Evaluate the function $h(x) = 1.5 e^x$ at the values $x = -1$, $x = \pi$, $x = 0.5$, and $x = \sqrt{2}$, rounding answers to two decimals.

1. **State the problem:** Find the equation of a line parallel to the line given by $$y = \frac{3}{4}x - 4$$ that passes through the point $(-2, -5)$. 2. **Recall the formula and r

1. **State the problem:** Find the equation of a line parallel to the line given by $$y = \frac{3}{4}x - 4$$ that passes through the point $(-2, -5)$. 2. **Recall the rule for para

1. **State the problem:** Evaluate the expression $$\frac{3}{4} \left( \frac{1}{3} + \frac{2}{7} \right)$$. 2. **Use the distributive property:** Multiply $$\frac{3}{4}$$ by the su

1. **Problem:** Calculate $\frac{3}{6} \times \frac{1}{4}$. Formula: Multiply numerators and denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$.

1. Задача 4.131: Сколько нужно взять последовательных натуральных чисел, кратных 3, чтобы их сумма была больше 165? Формула суммы первых $n$ членов арифметической прогрессии: $$S_n

1. **Stating av problemet (Oppgave 1a)** Vi har trapstallene $T_1=1$, $T_2=6$, $T_3=15$, $T_4=28$.

1. **State the problem:** Simplify the expression $4x^2 - 9$. 2. **Recognize the formula:** This expression is a difference of squares, which follows the formula:

1. The problem is to convert a fraction into a non-fraction (decimal or whole number) form. 2. To do this, we divide the numerator by the denominator.

1. The problem asks to solve for the values of $x$ in the equations given in parts 3 and 4 of the picture. 2. For part 3, the equation is $\frac{2x+3}{x-1} = 4$.

1. **Stating the problems:** a) Solve the inequality $$\lg^2(2x + 3) - 12\lg(2x + 3) + 20 \leq 0$$.

1. **State the problem:** We need to find the equation of the line shown on the graph in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 2. **Identify two

1. **State the problem:** Solve the system of equations: $$2x + y = 8$$

1. **State the problem:** Find the slope of the line given by the equation $y + 8x = 12$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $y = mx +

1. **State the problem:** Simplify the expression $$\frac{10^4 \times 5^3}{10^2 \times 5^5}$$. 2. **Recall the laws of exponents:**

1. **Stating the problem:** We have a 3x3 grid with mixed numbers and fractions, with cells labeled (a), (b), (c), and (d) empty. We need to find the values of (a), (b), (c), and (

1. **Stating the problem:** We have a 3x3 grid with fractions in most cells and labels (a), (b), (c), and (d) in some cells. The fractions given are mixed numbers and improper frac

1. **Problem 1:** Simplify $2b^4 - 3b^3 + 4b^4$ and classify the result. 2. Combine like terms: $2b^4 + 4b^4 = 6b^4$ and keep $-3b^3$ as is.

1. **State the problem:** We are given two functions: