Logarithm

Logarithm is the second chapter that can be found from the operation category. It provides methods and functions to operate logarithmic operations, including common logarithms, natural logarithms, exponential equation solving, and base conversions.

#include <imeth/operation/logarithm.hpp>

Features

Logarithm Functions

log(double base, double value) → std::optional<double> - Computes log_base(value) with arbitrary base
ln(double value) → std::optional<double> - Natural logarithm (base e)
log10(double value) → std::optional<double> - Common logarithm (base 10)
log2(double value) → std::optional<double> - Binary logarithm (base 2)

Exponential Equations

solve_exponential(double base, double value) → std::optional<double> - Solves base^x = value for x

Base Conversion

change_base(double value, double old_base, double new_base) → std::optional<double> - Converts logarithm from one base to another using the change of base formula

Return Values

All methods return std::optional<double>:

Contains a value if the operation is valid
Returns std::nullopt if:
- value ≤ 0 (logarithm undefined for non-positive numbers)
- base ≤ 0 (invalid base)
- base = 1 (division by zero in change of base formula)

Example Usage

#include <imeth/operation/logarithm.hpp>
#include <iostream>

int main() {
    // Basic logarithms
    auto result = imeth::Logarithm::log(2, 8);
    if (result.has_value()) {
        std::cout << "log_2(8) = " << result.value() << "\n";  // 3.0
    }

    // Natural logarithm
    auto ln_result = imeth::Logarithm::ln(2.718281828);
    if (ln_result.has_value()) {
        std::cout << "ln(e) ≈ " << ln_result.value() << "\n";  // ≈ 1.0
    }

    // Common logarithm
    auto log10_result = imeth::Logarithm::log10(1000);
    if (log10_result.has_value()) {
        std::cout << "log_10(1000) = " << log10_result.value() << "\n";  // 3.0
    }

    // Binary logarithm
    auto log2_result = imeth::Logarithm::log2(16);
    if (log2_result.has_value()) {
        std::cout << "log_2(16) = " << log2_result.value() << "\n";  // 4.0
    }

    return 0;
}

More Examples

// Solving exponential equations
// Solve: 2^x = 32
auto x = imeth::Logarithm::solve_exponential(2, 32);
if (x.has_value()) {
    std::cout << "x = " << x.value() << "\n";  // 5.0
}

// Solve: 10^x = 1000
auto x2 = imeth::Logarithm::solve_exponential(10, 1000);
if (x2.has_value()) {
    std::cout << "x = " << x2.value() << "\n";  // 3.0
}

// Change of base
// Convert log_2(8) to base 10
auto converted = imeth::Logarithm::change_base(8, 2, 10);
if (converted.has_value()) {
    std::cout << "log_10(8) = " << converted.value() << "\n";  // ≈ 0.903
}

// Error handling
auto invalid = imeth::Logarithm::log(2, -5);
if (!invalid.has_value()) {
    std::cout << "Cannot compute logarithm of negative number\n";
}

auto invalid_base = imeth::Logarithm::log(1, 10);
if (!invalid_base.has_value()) {
    std::cout << "Base cannot be 1\n";
}

Mathematical Properties

The logarithm functions implement standard mathematical properties:

Product rule: log(xy) = log(x) + log(y)
Quotient rule: log(x/y) = log(x) - log(y)
Power rule: log(x^n) = n·log(x)
Change of base: log_b(x) = log_a(x) / log_a(b)

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