Logarithmic equations involve log_b(x) = y, meaning b^y = x. Common forms: log₁₀(x) = y → x = 10^y. ln(x) = y → x = e^y. Change of base: log_b(x) = ln(x)/ln(b). Key properties: log(ab) = log(a)+log(b), log(a/b) = log(a)−log(b), log(aⁿ) = n·log(a).
How to Use
Choose equation form:
- log_b(x) = y: Find x
- log_b(a) = x: Find log value
- b^x = a: Find exponent
Common Bases
- Base 10 (log): common logarithm
- Base e (ln): natural logarithm
- Base 2 (lg): binary logarithm
Log Rules
- log(ab) = log(a) + log(b)
- log(a/b) = log(a) − log(b)
- log(aⁿ) = n·log(a)
- log_b(1) = 0
Step-by-Step Instructions
- 1Select equation form.
- 2Enter known values.
- 3Choose the base.
- 4View the solution.
- 5Check the verification.