Compute logarithms of a positive number in any base. Returns the custom-base logarithm, natural logarithm (ln), common logarithm (log10), and binary logarithm (log2). Useful for signal processing (decibel calculations), information theory (entropy in bits), pH chemistry, and general scientific computation. Uses the change-of-base formula log_b(x) = ln(x) / ln(b). Feeds into exponent_calc for inverse operations and scientific_notation for order-of-magnitude analysis.