Logarithm with any base
Find a log such as log base 2 of 20 by dividing two natural logs.
Most calculators only have log (base 10) and ln (base e) keys. The change-of-base rule fixes that: log base b of x equals ln(x) ÷ ln(b).
For log base 2 of 20 this gives ln(20) ÷ ln(2) = 4.321928095. Check: 2 to the power 4.32 is about 20.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Type ln(20) ÷ ln(2) and press enter.
ln20)÷ln2)enter
You should see4.321928095
Classic Scientific 30
Start on the main screen: Press 2nd then mode (QUIT) to leave any menu or screen and return to the calculation screen.
Type ln(20) ÷ ln(2) and press enter.
ln20)÷ln2)enter
You should see4.321928095
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
This model has a log-with-base template. Press the log□ key, type the base 2, press the right arrow, then type 20.
log2▶20Press =.
=
You should see4.321928095
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
Type ln(20) ÷ ln(2) and press EXE.
ln20)÷ln2)EXE
You should see4.321928095
The MATH menu (F4) also has a logab template.
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
The log key accepts a base as a second number. Type log(20, 2) and press ctrl enter.
log20,2)ctrl≈enter
You should see4.32193
RPN Scientific 15
Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.
Key in 20, press g and eˣ for LN. Key in 2, LN, and press ÷.
20gLNeˣ2gLNeˣ÷
You should see4.3219
RPN Advanced 42
Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.
Key in 20 and press LN, then 2 and LN, then ÷.
20LN2LN÷
You should seex: 4.3219
RPN Power 48
Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.
Key in 20 and press the right shift with yˣ for LN. Do the same for 2, then press ÷.
20▶LNyˣ2▶LNyˣ÷
You should see4.32192809488
Tips
- You can use log instead of ln in the formula. log(20) ÷ log(2) gives the same answer.