LOG1P(): log(1 + number)

<?Php
echo LOG1P(6);// Output is 1.9459101490553
echo "<br>";
echo LOG1P(-0.3);// Output is -0.35667494393873
echo "<br>";
echo LOG1P(0.4);// Output is 0.33647223662121
echo "<br>";
echo LOG1P(1.2);// Output is 0.78845736036427
?>

LOG1P(X);

Example 1: Calculating Compound Interest Using log1p()

<?php
$principal = 1000;
$rate = 0.05;
$time = 10;
$amount = $principal * exp($time * log1p($rate));
echo "Amount after 10 years: $amount";
?>

Example 2: Calculating Continuous Growth

<?php
$growth_rate = 0.03;  // 3% growth
$time = 7;  // over 7 years
$growth = exp(log1p($growth_rate) * $time);
echo "Total growth factor over 7 years: $growth";
?>

Example 3: Calculating Natural Logarithm for Positive and Negative Numbers

The log1p() function calculates the natural logarithm of 1 plus the given input. It’s particularly useful for numbers close to zero to avoid precision loss. Here's an example:

<?php
echo log1p(0.5); // Logarithm of 1.5
echo "<br>";
echo log1p(-0.3); // Logarithm of 0.7 (works for negative numbers too)
?>

Example 4: Use Case in Financial Calculations

log1p() can be used in compound interest calculations where precise computations of log values for small numbers matter:

<?php
$rate = 0.05; // 5% interest
$time = 10; // Time in years
$amount = log1p($rate * $time); 
echo "Logarithmic value: " . $amount;
?>

Example 5: Comparing log() vs log1p()

Comparing results for numbers close to zero:

<?php
echo log(1 + 1e-15); // Traditional log
echo "<br>";
echo log1p(1e-15); // log1p() provides better precision
?>

Subhendu Mohapatra

Author & Instructor at plus2net

I write and maintain practical tutorials on Python, PHP, SQL, JavaScript, HTML, jQuery, and web development at plus2net. The tutorials focus on clear explanations, working examples, and code that readers can test and adapt while learning.

About the author   Watch on YouTube

Connect: