4 Function Calculator with Log

log • ln Calculator
0
 

A 4 function calculator with log is a basic calculator that performs addition, subtraction, multiplication, and division and adds a log key for logarithms. You type a number, press the log key, and the calculator returns the exponent that base 10 must be raised to in order to produce that number. Many models add an ln key for the natural logarithm (base e).

3 Main Benefits of a Log Calculator

A Simple Keypad

The 4 operations plus the log keys.

Fast Log Results

No log tables needed.

Fewer Input Errors

Fewer input errors than a full scientific calculator.

Who uses it
🎓 Students 🧪 Chemistry learners ⚙️ Engineers 💼 Finance workers
What for
pH values Decibel levels Growth rates Exam practice
Overview

What Is a 4 Function Calculator With Log?

A 4 function calculator with log is a basic arithmetic calculator that adds logarithm keys to the 4 standard operations: addition (+), subtraction (−), multiplication (×), and division (÷).

Calculator type Log keys Other features Examples
Standard four-function ✗ No log key The 4 operations Canon LS-122TS desktop model
Four-function with log log ln Keeps the short keypad of a basic calculator and adds only the logarithm features This online calculator
Scientific ✓ log and ln Trigonometry, statistics, and memory functions Texas Instruments (TI) TI-30X IIS, Casio fx-115ES Plus, Sharp EL-531XT, Hewlett-Packard (HP) 35s

7 Main Components

The main parts are the number keys, the operation keys, the log key, the ln key, the equals key, the clear key, and the LCD screen.

0–9 .
Number KeysEnter digits 0 to 9 and the decimal point
+ − × ÷
Operation KeysRun addition, subtraction, multiplication, and division
log
Log KeyReturns the common logarithm (base 10)
ln
Ln KeyReturns the natural logarithm (base e)
±
Negative Sign KeySwitches a value between positive and negative
=
Equals & Clear KeysFinish a calculation or reset the display
3
LCD ScreenShows inputs, results, and error messages
How to Use

How to Use This Calculator With Log

To use this 4 function calculator with log, follow 5 steps.

  1. Clear the Display

    Press AC to reset the display.

  2. Enter a Positive Number

    Type a positive number, such as 1000.

  3. Press log or ln

    Press log for base 10, or ln for base e.

  4. Read the Result

    The result is 3 for log(1000).

  5. Combine for Multi-Step Calculations

    Combine the result with + − × or ÷ and press =.

Key Order Changes Between Devices

"log, then number"

Google Calculator and newer Casio and TI models.

log100=2
"number, then log"

Older pocket calculators and this online calculator.

100log2
Test the key order Test the order with log(100), which returns 2 on every correct entry.
Logarithm Basics

Understanding Logarithms

A logarithm is the exponent that a base must be raised to in order to produce a given number.

Logarithm form
logb(x) = y
log10(100) = 2
⇔
Exponent form
by = x
102 = 100
Log Explorer
Base
log10(1000) = 3
103 = 1000

x sits between the powers of the base shown on the scale.

A Short History of Logarithms

Log tables and the slide rule stayed the main calculation aids in engineering and science for about 350 years.

1614

John Napier published the first logarithm tables.

1624

Henry Briggs, an English mathematician, built base-10 logarithm tables and published Arithmetica Logarithmica.

1748

Leonhard Euler introduced the letter e for the natural base and defined the logarithm as the inverse of exponentiation.

1972

Electronic calculators such as the HP-35 replaced log tables and the slide rule.

Common Log (log₁₀) vs. Natural Log (ln)

The common log uses base 10, and the natural log uses base e (≈ 2.71828).

Feature Common Log Natural Log
Base 10 e ≈ 2.71828
Calculator key log ln
Example log(1000) = 3 ln(e) = 1
Main fields Chemistry, acoustics, seismology Calculus, finance, physics
The two logs convert with one factor
ln(x) = 2.302585 × log(x)

Example: ln(100) = 2.302585 × 2 = 4.60517

Change of Base

How to Calculate Log With a Different Base

To calculate log with a different base, divide the log of the number by the log of the base. This rule is the change-of-base formula.

Change-of-base formula
logb(x) = log(x) ÷ log(b) = ln(x) ÷ ln(b)

log₅(125) With the log Key

Common log path
  1. Log of the number
    log(125) = 2.09691
  2. Log of the base
    log(5) = 0.69897
  3. Divide
    2.09691 ÷ 0.69897 = 3
On this calculator
125log÷5log=3
Result
3

log₅(125) With the ln Key

The ln key gives the same result
  1. Ln of the number
    ln(125) = 4.82831
  2. Ln of the base
    ln(5) = 1.60944
  3. Divide
    4.82831 ÷ 1.60944 = 3
On this calculator
125ln÷5ln=3
Check
53 = 125
Examples

Examples of Log Calculations

There are 8 common log calculations that students and professionals check on a calculator with log.

Common Log

log(1000)
1000log
310³ = 1000

Common Log

log(0.01)
0.01log
−210⁻² = 0.01

Common Log

log(2)
2log
0.30103

Common Log

log(50)
50log
1.69897

Natural Log

ln(10)
10ln
2.302585

Natural Log

ln(1)
1ln
0

Log Base 2

log2(8)
8log÷2log=
32³ = 8

Log Base 2

log2(50)
50log÷2log=
5.64386

Example 1: pH in Chemistry

[H⁺] = 3.2 × 10⁻⁴ mol/L

A solution has a hydrogen ion concentration of 3.2 × 10⁻⁴ mol/L.

  1. pH equals the negative log of [H⁺]
    pH = −log(0.00032)
  2. The calculator returns
    log(0.00032) = −3.49485
pH
3.49 acidic solution

Example 2: Doubling Time in Finance

6% growth per year

An investment grows at 6% per year.

  1. Doubling time
    ln(2) ÷ ln(1.06)
  2. Divide the two natural logs
    0.693147 ÷ 0.058269
Doubling time
11.9 years
Real-Life Uses

Where Logarithms Are Used in Real Life

Logarithms are used in 6 main real-life fields.

Chemistry

Measures acidity with the pH scale.

pH=−log[H⁺]

Acoustics

Measures sound with the decibel (dB) scale.

100 × more powerful→+20 dB

Seismology

Rates earthquakes on a logarithmic scale.

+1 step→10× ground motionabout 32× more energy

Finance

Calculates compound interest periods, loan terms, and investment doubling times.

Computer Science

Uses log base 2 for binary search, data storage, and algorithm speed.

Statistics

Applies log transforms to skewed data, such as income or population figures.

Exams in the United States Students use a calculator with log for the SAT, the ACT, and AP exams, including AP Chemistry. The College Board and ACT, Inc. allow four-function and scientific calculators, and exam rules list the approved models.
Software tools Microsoft Excel uses the LOG, LOG10, and LN functions. Google Calculator, Desmos, GeoGebra, and Wolfram Alpha all support logarithm input online for free.
Specialized Tools

Explore Other Calculators

Need more than logarithmic functions? Pick the specialized calculator that matches your exact math needs.

½
With Fractions a/b • Mixed
±
With Negative Sign +/− Signed
📐
With Square Root √x Radicals
⚡
With Exponents x² • xʸ Powers
🧮
With Parentheses ( ) Grouping
📊
With Logarithm log • ln Functions
🔢
Decimal Calculator 0.00 Precision
FAQ

Frequently Asked Questions

Why does log of zero or a negative number show an error?

Log of zero or a negative number shows an error, since no real exponent turns a positive base into zero or a negative value. The value 10^y stays above zero for every real y. log(0) approaches negative infinity, and log(−5) exists only in complex numbers, which a 4 function calculator with log does not display.

The screen shows "Error," "Math ERROR," or "NaN" for these inputs.

What is the relationship between logs and exponents?

Logs and exponents are inverse operations. Exponentiation takes a base and an exponent and returns a number: 10³ = 1000. The logarithm takes the number and the base and returns the exponent: log₁₀(1000) = 3.

On a calculator with log and antilog, the 10^x key undoes the log key, and the e^x key undoes the ln key.

How do I calculate log base 2 on this calculator?

To calculate log base 2 on this calculator, divide log(x) by log(2). For log₂(64), press 64 log ÷ 2 log =. The calculator returns 1.80618 ÷ 0.30103 = 6, and 2⁶ = 64 confirms the result. The ln key works the same way: ln(64) ÷ ln(2) = 6.

Is "log" on a calculator base 10 or base e?

"Log" on most calculators is base 10, and "ln" is base e. Texas Instruments, Casio, Sharp, HP, Google Calculator, Desmos, and the Microsoft Excel LOG function (without a second argument) all treat log as base 10. Wolfram Alpha and several programming languages, including Python's math.log, treat log as the natural log.

Test the tool with log(10): a result of 1 means base 10, and a result of 2.302585 means base e.

Start Calculating Logarithms Now

Use this free online 4 function calculator with log. Add, subtract, multiply, divide, and compute logarithms — all in one tool. No downloads, no sign-ups.

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