Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks to find the value of the expression $((log_2 9)^2)^{\frac{1}{log_2(log_2 9)}} \time...
LogarithmsExponentiationAlgebraic Manipulation
2025/4/22
We are asked to solve the equation $\frac{2}{5x} - \frac{5}{2x} = \frac{1}{10}$ for $x$.
Algebraic EquationsSolving EquationsFractions
2025/4/22
The problem is to evaluate the expression $6 + \log_{\frac{3}{2}} \left\{ \frac{1}{3\sqrt{2}} \sqrt{...
LogarithmsQuadratic EquationsRadicalsAlgebraic Manipulation
2025/4/22
We need to simplify three logarithmic expressions: i) $log_10 5 + 2 log_10 4$ ii) $2 log 7 - log 14$...
LogarithmsLogarithmic PropertiesSimplification
2025/4/22
We are given a sequence $\{a_n\}$ defined recursively by $a_1 = 2$ and $a_{n+1} = 3a_n + 4$. The goa...
Sequences and SeriesRecurrence RelationsGeometric Sequences
2025/4/22
The problem describes a journey that takes place over three days. On the first day, 40% of the total...
Word ProblemPercentageLinear Equations
2025/4/22
The problem asks us to find the solutions of several equations. The equations are: a) $2x + 3 = -3 ...
EquationsLinear EquationsQuadratic EquationsFactoringComplex Numbers
2025/4/22
We are given two simultaneous linear equations: $x + y = 10$ and $y - 2x = 1$. We need to: a) Solve ...
Linear EquationsSystems of EquationsGraphing
2025/4/22
The problem asks to find all possible rational roots of the following polynomials: a. $f(x) = x^2 - ...
PolynomialsRational Root TheoremRootsFactoring
2025/4/22
We are asked to simplify the following inequalities: (a) $2x + 3 < 7$ (b) $5t + 6 > 21$ (c) $3x - 5 ...
InequalitiesLinear InequalitiesSolving Inequalities
2025/4/22