How to Put Log Base 4 in A Calculator

How to Calculate Log Base 4

The logarithm base 4 of a number x, written as log₄x, is the exponent to which the base 4 must be raised to obtain x. Mathematically, this is expressed as:

There are two primary methods to calculate log base 4: using a calculator directly or converting it to a common logarithm (base 10) using logarithm properties.

Using a Calculator

Most scientific calculators have a built-in logarithm function that can calculate log base 4 directly. Here's how to do it:

1. Turn on your calculator and ensure it's in the scientific mode.
2. Enter the number for which you want to calculate the logarithm (x).
3. Press the "log" button (this calculates log₁₀x).
4. Press the "÷" button.
5. Enter 4.
6. Press the "log" button again (this calculates log₁₀4).
7. Press the "=" button to get the result.

Manual Calculation

If you don't have a calculator, you can use the change of base formula and logarithm tables or a calculator for intermediate steps:

1. Find the common logarithm (base 10) of the number x (log₁₀x).
2. Find the common logarithm of 4 (log₁₀4 ≈ 0.60206).
3. Divide the result from step 1 by the result from step 2.

For more precise calculations, you can use natural logarithms (base e) with the formula: log₄x = lnx / ln4

Worked Examples

Let's calculate log₄16 using both methods.

Using a Calculator

1. Enter 16 on your calculator.
2. Press "log" to get log₁₀16 ≈ 1.20412.
3. Press "÷" and enter 4.
4. Press "log" to get log₁₀4 ≈ 0.60206.
5. Press "=" to get 1.20412 / 0.60206 ≈ 2.

Manual Calculation

1. From logarithm tables or a calculator, log₁₀16 ≈ 1.20412.
2. log₁₀4 ≈ 0.60206.
3. 1.20412 / 0.60206 ≈ 2.

The result is 2, which means 4² = 16.