Logarithm Simplifier
Algebra
Intro: We expand/condense logs with real numeric examples.
Worked example
- Expand $\log_2(8x^2/y)$
- Goal: Expand $\log_2(8x^2 / y)$ using logarithm rules.
- Step 1 — Recall the log quotient rule: $\log_b\left(\frac{M}{N}\right) = \log_b M - \log_b N$.
- Apply it here: $\log_2(8x^2 / y) = \log_2(8x^2) - \log_2(y)$.
- Step 2 — Now expand $\log_2(8x^2)$ using the log product rule: $\log_b(MN) = \log_b M + \log_b N$.
- So $\log_2(8x^2) = \log_2(8) + \log_2(x^2)$.
- Step 3 — Simplify $\log_2(8)$: since $8 = 2^3$, we get $\log_2(8) = 3$.
- Step 4 — Apply the log power rule: $\log_b(x^k) = k\log_b(x)$.
- So $\log_2(x^2) = 2\log_2(x)$.
- Step 5 — Put everything together:
- $$\log_2(8x^2 / y) = [\log_2(8) + \log_2(x^2)] - \log_2(y)$$
- $$= 3 + 2\log_2(x) - \log_2(y)$$.
- Final Answer: $\boxed{3 + 2\log_2(x) - \log_2(y)}$.
FAQs
Domains?
We assume positive arguments for logs.
Why choose Mathix?
- 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.
Log rules
- log₂(8x² / y) = log₂(8x²) − log₂(y)
- log₂(8x²) = log₂(8) + log₂(x²)
- Since 8 = 2³, log₂(8) = 3
- log₂(x²) = 2 log₂(x)
- Final result: 3 + 2 log₂(x) − log₂(y)