Logarithms

This program computes the logarithm of any number X to any base Y using the change-of-base formula: log_Y(X) = LN(X) / LN(Y). After displaying the result, it accepts a dummy keypress via INPUT W$ and then loops back to the start with RUN, allowing repeated calculations. Lines 9998–9999 are utility lines for saving and restarting the program and would not be reached during normal execution. The program relies entirely on the built-in natural logarithm function LN rather than any machine code or external routines.

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Program Analysis

Program Structure

The program is a simple, linear routine with an implicit loop created by RUN at line 130. There are no subroutines, no GO TO branching, and no conditional logic. Lines 9998–9999 are developer utility lines placed well beyond normal execution reach.

Lines	Purpose
10–30	Clear screen and display title/prompt
40–50	Input and echo the logarithm base Y
60–80	Input and echo the number X
90	Calculate the logarithm using change-of-base formula
100–110	Display the result
120–130	Wait for user input, then restart
9998–9999	SAVE utility and fallback RUN; never reached in normal flow

Core Algorithm

The change-of-base formula is implemented directly at line 90:

LET Z = LN X / LN Y

This correctly computes log_Y(X) for any positive base Y ≠ 1 and any positive X, relying entirely on the built-in LN (natural logarithm) function. No lookup tables or approximations are used.

Notable Techniques

• RUN as a loop: Line 130 uses RUN to restart the program from line 10, clearing all variables and providing a clean loop without needing a GO TO. This is a common Sinclair BASIC idiom.
• INPUT W$ as a pause: Line 120 uses INPUT W$ to hold the result on screen until the user presses ENTER, acting as a simple “press any key to continue” mechanism. Unlike PAUSE 0/INKEY$, this requires ENTER to proceed.
• Comma positioning: Lines 20, 30, 60, 100 use double commas (,,) in PRINT statements to advance to the third print zone, providing basic centred-ish formatting without AT or TAB.
• Echo of inputs: Lines 50 and 80 explicitly PRINT the entered values back to the screen, compensating for the fact that INPUT prompts on some Sinclair machines do not leave the entered value visible after acceptance.