Scientific Calculator Guide: When to Use Log, Ln, and Exponential Functions

Understanding Your Scientific Calculator Layout

Scientific calculators look intimidating, but they're organized logically. Most buttons fall into clear categories:

Basic Operations

+, −, ×, ÷, =, √, x², parentheses

Logarithms & Exponentials

log, ln, e^x, 10^x, antilog

Trigonometry

sin, cos, tan, and their inverses

Statistics & Memory

Σ, mean, standard deviation, M+, M−

LOG vs. LN: The Most Confusing Buttons Explained

This is the question that stumps everyone. Both are logarithms, but they use different bases. Understanding the difference is crucial.

LOG = Log Base 10

log(100) = 2

Because 10² = 100

When to use:

• pH calculations (chemistry)
• Decibel levels (physics)
• Richter scale (earthquakes)
• Orders of magnitude

LN = Natural Log (Base e)

ln(e) = 1

Because e¹ = e (≈2.718)

When to use:

• Compound interest (finance)
• Population growth (biology)
• Radioactive decay (physics)
• Calculus problems

Simple Rule of Thumb

• If the problem mentions e or involves continuous growth/decay → use ln

• If the problem mentions base 10 or involves powers of 10 → use log

• If unsure and it's a real-world application → probably ln (natural log is more common in science)

Exponential Functions: e^x and 10^x

These buttons are the inverses of logarithms. If logarithms ask "what power?", exponentials give you "the result of that power."

e^x

Euler's Number to the Power of x

Raises e (≈2.71828) to whatever power you enter. The inverse of ln.

Example: e^2 = 7.389...

Used for: Calculating compound interest, population predictions, solving differential equations

10^x

Ten to the Power of x

Raises 10 to whatever power you enter. The inverse of log.

Example: 10^3 = 1000

Used for: Converting log values back, scientific notation, pH to H+ concentration

Logarithms and Exponentials are Inverses

ln(e^x) = x

They cancel out

e^(ln(x)) = x

Works both ways

log(10^x) = x

Same for base 10

10^(log(x)) = x

Inverse relationship

Trigonometry Functions: Sin, Cos, Tan (And Their Inverses)

CRITICAL: Check Your Angle Mode!

Your calculator has modes: DEG (degrees) and RAD (radians). Using the wrong mode will give you totally wrong answers.

Use DEG for:

• Geometry problems
• Navigation
• Real-world angles (45°, 90°)

Use RAD for:

• Calculus
• Physics formulas
• Angles with π (π/2, 2π)

SIN (Sine)

In a right triangle: opposite side ÷ hypotenuse

Example: sin(30°) = 0.5

COS (Cosine)

In a right triangle: adjacent side ÷ hypotenuse

Example: cos(60°) = 0.5

TAN (Tangent)

In a right triangle: opposite side ÷ adjacent side (or sin ÷ cos)

Example: tan(45°) = 1

Inverse Trig Functions (sin⁻¹, cos⁻¹, tan⁻¹)

Also called arcsin, arccos, arctan. These work backwards—they give you the angle when you know the ratio.

Example: sin⁻¹(0.5) = 30°

(What angle has a sine of 0.5? Answer: 30 degrees)

Common Scientific Calculator Mistakes (And How to Avoid Them)

❌

Wrong Order of Operations

Wrong: Typing "2 + 3 × 4 =" and expecting (2+3)×4 = 20

Right: Calculator follows PEMDAS: 2 + (3×4) = 14. Use parentheses: "(2 + 3) × 4 = 20"

❌

Forgetting to Close Parentheses

Typing "(2 + 3 × 4" without closing gives weird results

Fix: Always close every "(" with a matching ")". Most calculators track your open parentheses count.

❌

Using DEG Mode for Calculus Problems

sin(π/2) in DEG mode gives -0.027, which is totally wrong

Fix: Switch to RAD mode for any problem with π. sin(π/2) in RAD = 1 (correct!)

❌

Confusing x² Button with x^y

x² button only squares. For other powers, use x^y or y^x button

Example: For 2⁵, type "2" then "x^y" then "5" then "="

❌

Not Clearing Before a New Problem

Previous calculation might still be in memory

Fix: Press "AC" (All Clear) or "C" before starting fresh. "AC" is safer—clears everything.

Advanced Features You Might Not Know About

📊ANS (Answer) Button

Recalls the result of your last calculation. Super useful for multi-step problems. Calculate "5 × 3 =", then type "ANS ÷ 2 =" to get 7.5.

💾Memory Functions (M+, M−, MR, MC)

Store values for later. M+ adds to memory, MR recalls it, MC clears it. Great for keeping running totals or intermediate results.

🔢SHIFT / 2nd Function

Buttons often have two functions. The second function (usually written above the button in a different color) is accessed with SHIFT or 2nd. Example: SHIFT + sin = sin⁻¹

⚙️MODE Button

Changes calculator settings: DEG/RAD, normal/scientific notation, floating/fixed decimals. Always check your mode before a test.