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