Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The image presents a chemical equation or a transformation involving symbols K, 15, 2 and an arrow. ...
EquationsVariablesSolving EquationsLinear Equations
2025/4/23
The problem is to solve the exponential equation $5 \times 2^{x-1} = 2 \times 5^{2x}$ for $x$.
Exponential EquationsLogarithmsEquation SolvingAlgebraic Manipulation
2025/4/23
The problem asks to solve the logarithmic equation $\log_a(2x+7) = \log_a x + 2\log_a 3$.
LogarithmsLogarithmic EquationsEquation Solving
2025/4/23
We need to solve the exponential equation $6^{1-T} = 5^{3T+1}$ for the variable $T$.
Exponential EquationsLogarithmsEquation SolvingLogarithm Properties
2025/4/23
The problem asks us to solve the exponential equation $4 \times 2^{2x+1} = 80$ for $x$.
Exponential EquationsLogarithmsEquation Solving
2025/4/23
Simplify the expression $4\log_3 2 - \log_3 4 - 2\log_3 \sqrt{3} - \log_3 12$ and write the final an...
LogarithmsLogarithmic PropertiesSimplification
2025/4/23
The problem asks to simplify the logarithmic expression $\log 8 + \log 5 - \log 0.5$ into a single l...
LogarithmsLogarithmic PropertiesSimplification
2025/4/23
We are asked to simplify the expression $3\log 8 - 3\log 6$ and express the result as a single logar...
LogarithmsLogarithm PropertiesSimplification
2025/4/23
Solve the exponential equation $3 \times 2^{x+1} = 24$ without using logarithms.
Exponential EquationsExponents
2025/4/23
The problem asks us to solve the exponential equation $(2x-3)^{-3/2} = 5$ without using logarithms.
ExponentsEquationsRadicalsSolving EquationsRationalization
2025/4/23