🧮 algebra

1. **State the problem:** Solve the equation $\log_3(9x) = 4x + 1$ for $x$. 2. **Recall the logarithm definition:** $\log_b(a) = c$ means $b^c = a$.

1. The problem is to solve the equation $\log_4(x^2) - 9 = 2$ for $x$. 2. Recall the logarithm property: $\log_b(a^c) = c \log_b(a)$.

1. **Problem Statement:** We need to determine which coupon, the 40% off or the 10 off coupon, gives the lower price for each item purchased.

1. **Problem Statement:** We have four items with prices: Bike $140, Scarf $18, Winter Coat $75, and Book $12. There are two coupons: a 10% off coupon and a $10 off coupon. We want

1. **Problem Statement:** We need to find the total seating capacity of a theatre with 40 rows of chairs. 2. **Given:**

1. Problem: Kayla runs 12 laps and is told she is 45% done. We need to find the total number of laps Kayla is trying to run. 2. Formula: To find the total, use the formula for perc

1. **Problem:** Kayla runs 12 laps and is told she is 45% done. We need to find the total number of laps Kayla is trying to run. 2. **Formula:** Percentage done = $\frac{\text{part

1. **Problem Statement:** (அ) Find the number of Singaporeans among the population.

1. Problem (iii): Find the remainder when $p(x)$ is divided by $3x + 1$. 2. To find the remainder when a polynomial $p(x)$ is divided by a linear divisor $ax + b$, use the Remainde

1. **Problem statement:** We are given the equation $$x^3 + y^3 + (x+y)^3 + 30xy = 2000$$ where $x,y \in \mathbb{Z}$ (integers). We need to find the value of $x+y$. 2. **Recall the

1. **Problem Statement:** Find the remainder when the polynomial $p(x)$ is divided by $3x + 1$. 2. **Recall the Remainder Theorem:** When a polynomial $f(x)$ is divided by a linear

1. **State the problem:** Solve the equation $7e^{2x} = 49$ for $x$. 2. **Recall the formula and rules:** We want to isolate $x$ in the exponential equation. Recall that $e^{a} = b

1. The problem is to find the value of $x + y$. 2. To solve this, we need values or expressions for $x$ and $y$.

1. **State the problem:** Solve the equation $$4^{2x+1} \cdot 16^{k-x} = \frac{1}{64^{x-3}}$$ for $x$ in terms of $k$. 2. **Rewrite bases as powers of 2:**

1. **Stating the problem:** We need to solve the equation $$x^3 + y^3 + (x+y)^3 + 30xy = 2000$$ where $x, y \in \mathbb{Z}$ (integers).

1. **State the problem:** Given the equations $a^2 - b^2 = bc$ and $\frac{b^2 - c^2}{ac}$, prove that $a^2 - c^2 = ab$ where $a,b,c \neq 0$. 2. **Analyze the given equations:** The

1. Problem 1: Determine the equation modeling the steel arches spanning a river 281 m wide with a height of 71 m. 2. The arch can be modeled as a parabola symmetric about the midpo

1. **State the problem:** Simplify the expression $$\sqrt{\frac{2^{22}}{2^{-4}}} \times 5 \sqrt{\left(\frac{2^{21}}{2^{2}}\right)^3}$$. 2. **Recall the rules:**

1. The problem states two exact sequences: $$0 \to A^\mu \to B^\nu \to C \to 0$$

1. **Solve the quadratic equation** $4x^2 + 9x + 5 = 0$. - Use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=4$, $b=9$, $c=5$.

1. The problem is to factorise the expression $x^2 - 16$. 2. This is a difference of squares, which follows the formula $a^2 - b^2 = (a - b)(a + b)$.