🧮 algebra

1. **State the problem:** Solve the logarithmic equation $$\log(x^2 + 5) - \log 3 = 1$$. 2. **Recall the logarithm property:** The difference of logarithms is the logarithm of a qu

1. **State the problem:** Solve the equation $10 \log(x + 21) + \log x = 2$ for $x$. 2. **Recall logarithm properties:**

1. **State the problem:** Solve the equation $$\ln 8 - \ln (-2x) = \ln 13$$ for $x$. 2. **Recall the logarithm property:** The difference of logarithms is the logarithm of the quot

1. **State the problem:** Solve the logarithmic equation $$8 \log_7 (x^2 - 1) - \log_7 5 = 1$$ for $x$. 2. **Recall logarithm properties:**

1. **State the problem:** Solve the equation $\log_2 (x + 4) - 2 \log_2 5 = 4$ for $x$. 2. **Recall logarithm properties:**

1. **State the problem:** Solve the equation $$\log_{12}(k - 10) + 5 = 4$$ for $k$. 2. **Isolate the logarithmic term:** Subtract 5 from both sides:

1. **State the problem:** Solve the equation $$-9 \log_3 -4p = -27$$ for $p$. 2. **Rewrite the equation:** The equation is $$-9 \log_3 (-4p) = -27$$.

1. نبدأ بكتابة المسألة: لو90 – 3 لو10 3 2. نستخدم خاصية اللوغاريتمات التي تقول: \(\log_a b^c = c \log_a b\)

1. The problem is to solve the equation or expression given by the user, but since no specific equation or expression was provided, I cannot solve a particular problem. 2. Please p

1. The problem is to understand how to factorize algebraic expressions. 2. Factorization means writing an expression as a product of its factors.

1. **Problem statement:** Simplify the expression \(\frac{(x-a)(x-b)}{(c-a)(c-b)} + \frac{(x-b)(x-c)}{(a-b)(a-c)} + \frac{(x-c)(x-a)}{(b-c)(b-a)}\). 2. **Formula and approach:** Th

1. The problem is to evaluate $\log_{90} 3 \times \log_{10} 3$. 2. Recall the change of base formula: $\log_a b = \frac{\log_c b}{\log_c a}$ for any positive $c \neq 1$.

1. **Nyatakan masalah:** Kita diberi maklumat tentang perkongsian hartanah dan beberapa soalan berkaitan pecahan dan pengiraan. 2. **a. Bilangan rumah yang akan dibina:**

1. **State the problem:** Given $x>0$, $y>0$, and the equation $$y^3 \cdot x^{\log_{10}(x)} = 10,$$ find the maximum value of $$x^2 y.$$\n\n2. **Rewrite the constraint:** Note that

1. **Problem statement:** Rita and Henry share profits in the ratio 3:5. Henry's profit is 24500. Find Rita's profit. 2. **Formula and rules:** If two quantities share a total in r

1. **State the problem:** We need to find the minimum and maximum values of the function $$f(x) = 10x^2 - \lg x$$ for $$1 \leq x \leq 1000$$. 2. **Recall the function and domain:**

1. **State the problem:** We are given the function $y=\log_5(x-10)$ with the domain $3 \leq x \leq 5$. We need to find the minimum and maximum values of $y$ on this domain. 2. **C

1. **Problem Statement:** We have two taxi services with costs represented by parallel lines on a graph. The Speedy Taxi Service charges a base cost of $1.80 plus $0.10 per kilomet

1. نبدأ بكتابة المعطيات: لدينا المعادلة $$ س = 4 + ص $$ وشرط $$ س \neq 0 $$. 2. المطلوب هو التحقق من صحة المعادلة $$ \frac{ص^2}{س} = 2 $$.

1. **State the problem:** We have a function $$y = -x^2 + 2(\log(2)a)x + \log(2)b$$ defined for $$0 \leq x \leq 4$$. The maximum value of the function is 5 and the minimum value is

1. **State the problem:** Simplify the expression $$(3x^3 - 2x + x^2) - (x^2 + x^3)$$. 2. **Write down the expression clearly:**