Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are given two equations: 1. $\log y = 2 \log x + 1$

LogarithmsQuadratic EquationsSystems of EquationsSubstitution
2025/3/17

Solve the following system of equations: $\log y = 2 \log x + 1$ $2y = 9x - 1$

Systems of EquationsLogarithmsQuadratic EquationsSolution Verification
2025/3/17

We are given two equations: $\log y = 2 \log x + 1$ and $2y = 9x - 1$. We need to solve for $x$ and ...

LogarithmsQuadratic EquationsSystems of EquationsSubstitutionFactorization
2025/3/17

The problem asks us to solve three logarithmic equations for $x$. (a) $\log_{10}(x^2 + 13x) = 1 + \l...

Logarithmic EquationsSolving EquationsAlgebraic Manipulation
2025/3/17

We are given two logarithm problems to solve for $x$. Problem 5: Find $x$ if $\log_{10}(2x+1) - \log...

LogarithmsEquationsSolving EquationsLogarithmic EquationsAlgebraic Manipulation
2025/3/17

The image presents two problems. Problem 3 asks to solve the equation $\log_2(x+2) = \log_2(x-1) + 1...

LogarithmsEquationsLogarithmic EquationsSolutionProperties of Logarithms
2025/3/17

The problem asks to express each given expression as a single logarithm. (a) $2log_a5 + log_a4 - log...

LogarithmsLogarithmic PropertiesProduct RuleQuotient RulePower Rule
2025/3/17

We are given the values of $\log a$, $\log b$, and $\log c$, and we are asked to evaluate four logar...

LogarithmsLogarithm PropertiesExponents
2025/3/17

Given that $a$, $b$, and $c$ are non-zero, solve the equation $\frac{a}{b} = 2c$ for $b$.

Equation SolvingLinear EquationsVariablesAlgebraic Manipulation
2025/3/17

The problem asks us to find the general term $a_n$ of a sequence defined by the recurrence relation ...

Recurrence RelationsSequencesGeometric SequencesAlgebraic Manipulation
2025/3/17