Exponential & Log Equation Solver
Algebra, Exponents & Logs
Intro: Solves basic exponential and logarithmic equations, isolating x and showing each algebraic step.
Worked example
- Solve the exponential equation $2^x = 10$.
- We want to solve $2^x = 10$ for x.
- Take the natural logarithm (or any log) of both sides: $\ln(2^x) = \ln(10)$.
- Use the power rule for logs: $\ln(2^x) = x\ln(2)$.
- So the equation becomes $x\ln(2) = \ln(10)$.
- Solve for x by dividing both sides by $\ln(2)$: $x = \dfrac{\ln(10)}{\ln(2)}$.
- Compute a decimal approximation: $\ln(10) \approx 2.3026$ and $\ln(2) \approx 0.6931$.
- Thus $x \approx 2.3026 / 0.6931 \approx 3.322$.
- Answer: $\boxed{x = \dfrac{\ln(10)}{\ln(2)} \approx 3.32.}$
FAQs
Can this solver handle multiple logs in one equation?
Yes, for typical homework-style equations it applies log rules and algebra steps. Very complex equations may need manual simplification.
Why choose MathGPT?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.