Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

Solve the equation $2\log{x} - \log{4} = 2$. We assume the base of the logarithm is 10.

LogarithmsEquationsAlgebraic ManipulationSolving Equations

The problem states that 10% of 20% of a is equal to 30% of 40% of b. We need to find what percentage...

PercentageAlgebraic EquationsVariable SubstitutionSolving Equations

The problem asks us to simplify the expression $log_3 a - (log_3 b + log_3 c)$ into a single logarit...

LogarithmsLogarithm PropertiesSimplification

We are given the function $f(x) = \frac{3x^2 - x}{x - 1}$ and asked to find the equation of its obli...

AsymptotesRational FunctionsPolynomial Long Division

We are asked to solve the equation $5^{2-x} = \frac{1}{125}$ for $x$.

ExponentsEquationsExponential EquationsAlgebraic Manipulation

In a classroom, 40% of the students are male. If 25% of the female students are absent, only 27 fema...

PercentageWord ProblemLinear Equations

The problem asks to write the expression $\frac{1}{2} [4 \log x - \log \sqrt{x^5}] + \log \sqrt[3]{x...

LogarithmsAlgebraic ManipulationSimplification

We are given two functions, $f(x) = log_{10}x$ and $f(x) = -\frac{1}{2}log_{10}x - 5$. We need to de...

LogarithmsFunction TransformationsVertical CompressionReflectionVertical Translation

We are given that $84\%$ of $N$ is equal to $105\%$ of $(N-120)$. We need to find what percentage of...

PercentageEquationsSolving EquationsLinear Equations

The problem states that $M$ is 150% of $N$. We need to find what percentage $N$ is of $M+N$.

PercentageRatioEquation Solving

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