TI-89HOW TO
Logs, Roots, Exponents and Factorials on the TI-89 Titanium
Searches like how to do log on the TI-89 come up so often because the keypad hides several basic functions behind ◆ and 2nd, and one of them has no key at all. This article shows where log, ln, e, square roots, cube roots, exponents and the factorial sign are on the TI-89 Titanium, how to type each one, and what the CAS returns.
How to do log on the TI-89
There is no LOG label printed on the TI-89 Titanium keypad. The common log is still built in: type the letters l, o, g and an opening parenthesis with alpha, or open CATALOG, jump to L and pick log(. The answer stays exact, as the first row below shows.
Calc89 also has a shortcut for it: ◆ 7 enters log( directly. Command page: log(.
| Input | Result |
|---|---|
| log(1000) | 3 |
| log(x)▶ln | ln(x)/ln(10) |
The second row converts a log into natural logs, which is the change of base rule written out by the CAS.
Log base 2 and other bases
For any base b, use the change of base rule: logb(x) = ln(x)/ln(b). On the handheld that means typing ln(8)/ln(2) for log base 2 of 8. Calc89 accepts a second argument as the base, log(8,2), and it also has the conversion ▶logbase(.
Natural log and e
ln( is the 2nd function of the X key. Its inverse, e to a power, is the ◆ function of the same key and enters ℯ^( with the parenthesis already open. For the constant e on its own, type ℯ^(1). Do not use the alpha letter e: that is just a variable named e.
| Input | Result |
|---|---|
| ln(ℯ) | 1 |
| cosh(x)▶exp | (ℯx+ℯ−x)/2 |
The first row is the check you can always use: ln(ℯ) is 1. The second shows ℯ in an exact result, rewriting cosh(x) with exponentials.
Exponents with the ^ key
Every power goes through the ^ key on the right side of the keypad. The TI-89 Titanium has no separate x² key, so a square is ^2 and a cube is ^3. Put anything longer than a single number or letter in parentheses: 2^(x+1), not 2^x+1. For a negative exponent, use the (−) key, not the subtraction key: x^(-2). Powers of ten are typed the same way, 10^(3).
| Input | Result |
|---|---|
| expand((x+1)^2) | x2+2·x+1 |
| seq(n^2,n,1,5) | {1,4,9,16,25} |
Both rows keep the powers exact: the first expands a square, the second lists the squares of 1 to 5.
Square roots and cube roots
√( is the 2nd function of the × key. The CAS simplifies roots instead of giving a decimal, so √(8) comes back as 2·√(2). Press ◆ ENTER when you need the decimal.
For a cube root on the handheld, raise to the power one third, with the fraction in parentheses: 27^(1/3). Without the parentheses, 27^1/3 means 27 divided by 3. Any nth root works the same way with 1/n. Calc89 adds root(, which takes the value and the index: root(27,3).
| Input | Result |
|---|---|
| √(8) | 2·√2 |
| root(27,3) | 3 |
Factorials
The factorial sign is ◆ ÷. Type the number first and the sign after it, as in 5!, then press ENTER. The ! also sits in the Probability submenu of MATH (2nd 5), next to nPr( and nCr(, which are built from factorials.
| Input | Result |
|---|---|
| nCr(5,2) | 10 |
| nPr(5,2) | 20 |
| gamma(5) | 24 |
The gamma function extends the factorial to non integers: for a whole number n, gamma(n) equals (n − 1)!, so the last row is 4!. Calc89 offers gamma( as a command; on the handheld, use ! for whole numbers.
Common mistakes
- Missing parentheses in exponents. 8^1/3 is 8 divided by 3, not a cube root.
- The letter e instead of ℯ. Use ◆ X; the alpha e is a variable.
- Subtraction instead of (−). A negative exponent needs the (−) key.
- Expecting decimals. log, ln and √ stay exact. Press ◆ ENTER for a decimal.
- A stored x. If x holds a number, expressions with x evaluate to numbers. Run NewProb (2nd F1) to clear it.
In Calc89
Calc89 is a CAS calculator app intended for use with TI-89 Titanium. LN, ℯ^(, √(, ^ and ! sit on the same keys as on the handheld, and Calc89 adds ◆ 7 for log( as well as log( with a base and root( for any index. Results stay exact, just like above. If a log or root problem is printed in your book, scan it with the camera instead of typing nested parentheses. The keystroke tutor shows the exact key sequence for the TI-89 Titanium, step by step, which helps when you have to do the same calculation on the handheld in class. Calc89 is free to download, Pro features as an in-app purchase.
For the whole keypad, including the 2nd, ◆ and alpha layers, see The TI-89 Titanium keypad explained.
Frequently asked questions
Is there a log button on the TI-89 Titanium?
No LOG label is printed on the keypad, only LN above the X key. Type log( with the alpha letters or pick it from CATALOG. In Calc89, ◆ 7 enters log( directly.
How do I type a cube root on the TI-89?
Raise the number to the power 1/3, with the fraction in parentheses: 27^(1/3). In Calc89 you can also use root(27,3).
Where is the factorial key on the TI-89 Titanium?
Factorial is ◆ ÷. Type the number first, then ◆ ÷, for example 5!.
Where is e on the TI-89?
◆ X enters ℯ^( for powers of e. For the constant alone, use ℯ^(1). LN on 2nd X is its inverse.
Related pages
- /commands/log/
- /commands/ln/
- /commands/sqrt/
- /commands/root/
- /commands/gamma/
- /commands/ncr/
- /guides/ti-89-keystrokes-basics/
More from the blog
- TI-89 Titanium vs TI-Nspire CAS: Which CAS Do You Need for Engineering?Keys, display, documents, CAS power and exam rules: how the TI-89 Titanium and the TI-Nspire CAS differ, and which one fits engineering.
- TI-89 vs TI-84 for Calculus: What a CAS AddsExact symbolic answers versus numeric ones, side by side: what the TI-89 Titanium adds over the TI-84 and when each one makes sense.
- Taylor Series, Sums and Sequences on the TI-89taylor( for Taylor polynomials, Σ( for sigma notation, sum( and seq( for lists, plus partial sums, products and infinite series on the TI-89 Titanium.