Solve logarithmic equations, expand/condense log expressions, change bases, and get detailed step-by-step solutions. Master logarithms with AI-powered explanations.
logb(x) = y
Solve logarithmic problems:
Choose an operation and enter your logarithmic expression to get detailed step-by-step solutions.
Format: logb(x) = y
log₁₀(100) = 2
Basic logarithm
log₂(8) = 3
Binary logarithm
ln(e³x²)
Natural log expansion
log₂(8) → log₁₀(8)
Base change
Solving logarithmic expression...
log₁₀(100) = 2
Solution:
2
Verification:
10² = 100 ✓
Logarithm Form:
log₁₀(100) = 2
Exponential Form:
10² = 100
Used Properties:
Definition of logarithm
Product Rule:
logₐ(xy) = logₐ(x) + logₐ(y)
Quotient Rule:
logₐ(x/y) = logₐ(x) - logₐ(y)
Power Rule:
logₐ(xⁿ) = n·logₐ(x)
Solve logarithmic equations, expand complex log expressions, condense multiple logs into one, or change between different bases with ease.
Visualize logarithmic functions with interactive graphs. Adjust the base and range to understand how different parameters affect the curve.
Get detailed step-by-step solutions with clear explanations of each logarithm rule applied. Learn the concepts, not just the answers.
A logarithm answers the question: "To what exponent must we raise a base number to get another number?" For example, in the equation log₁₀(100) = 2, this means 10² = 100. The logarithm is the exponent (2) to which the base (10) must be raised to produce the number (100).
The three main logarithm rules are:
There's also the Change of Base Rule: logₐ(x) = logₑ(x) / logₑ(a) = ln(x) / ln(a)
log (without a base specified) usually means logarithm base 10, also called the common logarithm. ln means natural logarithm, which has base e (approximately 2.71828). In mathematics, ln is more common because e has special properties in calculus and growth/decay problems.
Logarithms are used in many real-world applications:
Yes, our logarithm solver can handle complex expressions including:
The AI will provide step-by-step explanations for even the most complex logarithmic problems.
Select what you want to do: solve an equation, expand a logarithm, condense multiple logarithms, or change the base of a logarithm.
Input your logarithmic expression in the appropriate format. Use the examples as a guide if you're unsure about the format.
Press the "Solve & Explain" button and our AI will process your logarithmic expression, providing the solution and detailed explanations.
View the summary of results, examine the logarithm properties used, follow the step-by-step solution, and visualize the function graph.
Use the "Load Example" button to see different types of logarithmic problems. Try clicking on the quick examples to automatically load and solve different logarithm types.