Logarithm Equation Solver
Solve logₐ(x) = y
Find x given log base a of x equals y
Solve logₐ(x) = y for base a
Find the base given x and y
Change of Base
Convert logₐ(x) to different bases
Logarithm Properties
Apply log properties: product, quotient, power rules
Formula
logₐ(x) = y ↔ aʸ = x | Change of base: logₐ(x) = ln(x)/ln(a) | Product: log(ab) = log(a)+log(b)
Frequently Asked Questions
How do you solve logarithmic equations?
Convert to exponential form: logₐ(x) = y means aʸ = x. Use properties to combine or separate logs. The change of base formula logₐ(x) = ln(x)/ln(a) converts between bases.
What is the change of base formula?
logₐ(x) = logᵦ(x) / logᵦ(a). This lets you calculate any logarithm using a calculator's built-in log₁₀ or ln buttons. For example, log₅(100) = log₁₀(100)/log₁₀(5) = 2/0.699 ≈ 2.861.
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