So you need to put the number below log? Man, I remember scratching my head over this back in college. My professor kept saying "log base 10" like it was obvious, but when I looked at my calculator, there was only one log button. Where does that little base number actually go? Turns out it's different for every device and program. Let's break this down together.
Short answer: There's no universal method. For calculators, you'll usually find a "logb( )" button or need to type the base first. In Excel, use =LOG(number, base). For handwriting, write "log" then small subscript. Keep reading for device-specific breakdowns.
Handwriting Logarithms Correctly
When writing by hand, putting the number below log means creating a subscript. Like this: log10100 = 2. That little 10 is your "base" number. But here's the trick most guides won't tell you: handwriting this clearly requires technique.
I ruined so many lab reports before learning these tips:
- Write the full word "log" normally
- Drop your pen slightly below the baseline
- Make the base number 50% smaller than regular text
- Keep it vertically aligned with the "g"
Mess up the alignment and it becomes ambiguous. Is that log base 10 or log times 10? Been there. My chemistry TA once deducted points because my bases looked like regular numbers.
Calculator Methods: Brand by Brand
Trying to put the number below log on a calculator? Good luck finding consistency. Every brand does it differently. Here's what I've learned from using dozens of models:
Casio Scientific Calculators
On most Casios (like the fx-300ES), press the "SHIFT" button first. Then hit the log key – it'll show "log□(□)". Use arrows to navigate between boxes.
| Model | Steps to Input Base | Annoying Quirk |
|---|---|---|
| fx-300ES | SHIFT → log → enter base → right arrow → enter number | Forgets your base after each calculation |
| fx-991EX | Press "log" → select base template → fill boxes | Touchscreen gets fingerprints everywhere |
Watch out: On older Casio models, log always assumes base 10. You'll need to use the change-of-base formula manually. Total pain during exams.
Texas Instruments (TI-84 Plus)
I love my TI-84, but their log input feels clunky:
- Press MATH
- Scroll to "logBASE("
- Type base → press → arrow
- Type number → close parenthesis
Why do they bury it three menus deep? Feels intentional. Takes twice as long as Casio's method.
Software Solutions
Okay, but how to put the number below log when working digitally? Different rules apply.
Microsoft Excel & Google Sheets
Finally, something straightforward! Use this formula:
- =LOG(number, base)
- Example: =LOG(27,3) returns 3
But I've got gripes. Why doesn't Excel display the base visually? It just shows the result. You'll lose track if you're doing multiple logs.
| Software | Proper Syntax | Special Case Handling |
|---|---|---|
| Excel | =LOG(number, base) | Base defaults to 10 if omitted |
| Google Sheets | =LOG(value, base) | Returns #NUM! error for base=1 |
| Apple Numbers | LOG(number, base) | No automatic base conversion |
Programming Languages
Coding logarithms? Most languages only include natural log (ln) and base-10 log out of the box. To put the number below log with custom bases:
| Language | Custom Base Code | What Developers Often Mess Up |
|---|---|---|
| Python | import math math.log(x, base) |
Forgetting negative bases crash the program |
| JavaScript | Math.log(x) / Math.log(base) | Sloppy parentheses causing wrong results |
| C++ | #include log(x)/log(base) |
Not handling division-by-zero errors |
Pro Tip: In Python, math.log(x, base) is cleaner than division. But it runs slower for massive datasets. Weird trade-off.
Advanced Scenarios
What if you're dealing with unconventional bases? Through trial and error (mostly error), I've figured out these situations.
Fractional Bases
Logarithms with fractional bases work differently. To put the number below log when base is between 0 and 1:
- Example: log1/2(8) = -3
- On calculators: Enter as decimal (0.5)
- In Excel: =LOG(8, 0.5)
But watch your parentheses! log1/28 ≠ log(1/2)*8. That mistake ruined my entire statistical model once.
Physical Calculators vs. Mobile Apps
Mobile calculator apps confuse people about how to put the number below log. Comparison:
| Platform | Base Input Method | Real-World Usability |
|---|---|---|
| iPhone Calculator | Rotate phone → scientific mode → long-press log | Horrible for quick calculations |
| Google Calculator App | Tap ∰ → logb → enter values | Best mobile implementation I've seen |
LaTeX and Academic Writing
When typing documents, use this LaTeX code for proper log formatting:
- \log_{base}number → logbasenumber
- Example: \log_{3}81 renders as log381
But Word processors? They make it needlessly complicated. In Microsoft Word:
- Type "log"
- Select "Subscript" (Ctrl+=)
- Type base number
- Click subscript again to exit
- Type main number
Good luck maintaining consistent font sizes. Half my base numbers end up microscopic.
Common Mistakes and Fixes
After tutoring math students for five years, I've seen every possible error when learning how to put the number below log.
Critical Warning: Never assume log means base 10 in programming. In Python, log() is natural log. In Excel, it's base 10. This inconsistency causes serious calculation errors.
Top 3 screw-ups I constantly correct:
- Base Position Ambiguity: Writing log10x instead of log10x
- Calculator Confusion: Inputting base where exponent should go
- Syntax Errors: Forgetting commas in Excel formulas
Real talk: The Texas Instruments manual might as well be hieroglyphics. Here's simpler instructions:
- Identify if you're using calculator, software, or handwriting
- Locate the base input location (subscript/template/second parameter)
- Enter base BEFORE the main number in most interfaces
Frequently Asked Questions
Q: Can I put letters below the log?
A: Absolutely. In algebra, logba is common. Same input methods apply. But calculators usually require numerical bases.
Q: Why won't my calculator accept negative bases?
A: Because logarithms with negative bases involve complex numbers. Most basic calculators lack this functionality. Use software like MATLAB instead.
Q: How to put multiple numbers below log?
A: You don't. The base is always a single number. If you see logxy, it likely means logxy. Poor notation causes this confusion.
Q: Is there a shortcut for common bases?
A: Yes! Most calculators have dedicated buttons:
- ln for base e
- log for base 10
- Sometimes lb for base 2
Q: How to put the number below log in graphing?
A: Graphing requires different approaches. On TI calculators, use the logBASE template. In Desmos, type "log_b(x)" then define b separately.
Special Cases You Should Know
Sometimes standard methods fail. Here's how professionals handle edge cases:
| Situation | Proper Approach | Workaround When Stuck |
|---|---|---|
| Base = 1 | Undefined mathematically | Return error message in code |
| Base = 0 | Not possible | Input validation in programs |
| Negative arguments | Complex number result | Use cmath module in Python |
Insider Tip: When using change-of-base formula (logba = ln a / ln b), watch floating-point errors in programming. They compound.
Verifying Your Results
After learning how to put the number below log, always verify. Here's my sanity-check routine:
- For logba = c
- Compute bc
- Should approximately equal a
Example: log381 = 4 → 34 = 81 ✓
If results don't match, likely causes:
- Base input in wrong location
- Syntax error in formulas
- Calculator in wrong mode (degrees vs radians doesn't affect logs but indicates setup issues)
Final thought: Mastering how to put the number below log takes practice across different tools. Start with handwriting, then progress to calculators, then coding. Each requires different muscle memory. Don't get discouraged if TI-84 input feels awkward at first – even professors struggle with it.
Comment