Logarithm Calculator with Equation Solver

Logarithm Basics

The logarithm log_a(b) answers the question: "What exponent do I need to raise a to get b?"

a^x = b
x = log_a(b)

The Four Logarithm Laws

The laws of logarithms are a straightforward set of rules that simplify the manipulation of logarithmic expressions.

1. Product Rule: log_a(x) + log_a(y) = log_a(x * y)
2. Quotient Rule: log_a(x) - log_a(y) = log_a(x / y)
3. Power Rule: log_a(x^k) = k * log_a(x)
4. Change of Base: log_a(b) = log_c(b) / log_c(a)

Simplify Expressions

Enter a logarithmic expression that can be simplified using the logarithm laws.

Supported formats:
log2(8) + log2(4) ? Product rule
2 * log10(5) ? Power rule
log(100) - log(10) ? Quotient rule
log2(8) ? Direct calculation

Solve Logarithm Equations

Enter a logarithmic equation to solve for x. The calculator supports various equation types.

Examples:
log2(x) = 3
log(x) + log(x+1) = 1
2 * log3(x) = 4
log2(x) = log2(8)
log(x) = 2

Calculation History