🧮 algebra

1. The problem is to solve the equation $$\log_3(x + 4) = 2$$ and analyze the function $$f(x) = -\log_3(x + 2)$$. 2. To solve $$\log_3(x + 4) = 2$$, recall that $$\log_b(a) = c$$ m

1. The first expression is $f(x) = \log_2(x)$. This is a logarithmic function because it defines $f(x)$ as the logarithm of $x$ with base 2. 2. The second expression is $\log_2(x)

1. Let's start by defining each term clearly. 2. A **logarithmic equation** is an equation that involves a logarithm with a variable inside it, for example, $\log_b(x) = y$ where $

1. The first expression is $2\log_{10}(x) = \log_{10}(50)$. This is an equation involving logarithms, so it is a **logarithmic equation**. 2. The second expression is $\log_3(x + 1

1. **State the problem:** We want to show that the recurring decimal $0.28\overline{13}$ equals the fraction $\frac{557}{1980}$. 2. **Express the decimal as a sum:** Let $x = 0.28\

1. **State the problems:** We have three problems involving logarithms:

1. Problem: Solve the equation $x + (x + 2) = 67$ to find $x$. 2. Combine like terms: $x + x + 2 = 67$ simplifies to $2x + 2 = 67$.

1. Problem 9: A farmer initially wants to build a square fence with side length 12 m. The perimeter of this square is $$P = 4 \times 12 = 48\text{ m}$$.

1. **Problem 3:** Given the function $h : x \to px - q$ with $h(-3) = -13$ and $h(2) = -3$, find: (a) The values of $p$ and $q$.

1. Masalah 18: Tentukan banyak produk per hari agar biaya operasional kedua mesin sama. Misalkan $x$ adalah banyak produk per hari.

1. Masalah 6: Berat 1 karung apel dan 1 karung mangga adalah 67 kg. Berat 1 karung apel 3 kg lebih berat dari 1 karung mangga. Tentukan berat masing-masing karung. 2. Misalkan bera

1. **State the problem:** XYZ Company bought a machine for 50000. Profits start at 7876 in March and increase by 2% each month. We want to find the month when total profits pay off

1. **Énoncé du problème :** Nous étudions la fonction $f(x) = \sqrt{x+1}$.

1. The problem states that Mya converted some amount in pounds (£) to Danish kroner (kr) at an exchange rate of £1 = 8.50 kr. 2. We know she received 867 kr after conversion.

1. **State the problem:** Betty paints twice as fast as Dan. Together, Dan and Betty paint 2400 square feet in 4 hours. Sue joins them, and all three paint 3600 square feet in 3 ho

1. נתחיל מהביטוי הנתון: $5y^{29} - 20m^4$ 2. נבדוק אם יש גורם משותף לשני האיברים. נראה כי $5$ הוא גורם משותף.

1. **State the problem:** A baker starts with $\frac{3}{4}$ cup of water. 2. He pours half of the water into the batter, so the amount poured is:

1. נתחיל מהביטוי הנתון: $125y^2 - 180m^4$ 2. נזהה גורם משותף למקדמים: $125$ ו-$180$ שניהם מתחלקים ב-$5$.

1. **State the problem:** Annie bought 17 articles consisting of books and pens for a total cost of 25000. Each book costs 2000 and each pen costs 1000. We need to find the fractio

1. **State the problem:** We have three types of bags: wheat (W), corn (C), and oats (O). The problem gives us relationships between their weights and asks for the weight of one ba

1. The problem asks us to find which box of pens has the cheapest cost per pen. 2. We calculate the cost per pen for each box by dividing the total cost by the number of pens: