Logarithmic Calculations (log, ln)

Logarithms in the Evaluator

The evaluator provides two logarithm functions:

• log(x) -- base-10 (common) logarithm
• ln(x) -- base-e (natural) logarithm

Base-10 Logarithm

The common logarithm answers "10 raised to what power gives x?"

log(10)    = 1     (10^1 = 10)
log(100)   = 2     (10^2 = 100)
log(1000)  = 3     (10^3 = 1000)
log(1)     = 0     (10^0 = 1)
log(0.01)  = -2    (10^-2 = 0.01)

Natural Logarithm

The natural logarithm uses Euler's number e (approximately 2.71828) as its base:

ln(e)      = 1     (e^1 = e)
ln(1)      = 0     (e^0 = 1)
ln(e^2)    = 2
ln(2)      = 0.693
ln(10)     = 2.303

Converting Between Bases

You can convert from one base to another using the change-of-base formula:

log_b(x) = ln(x) / ln(b)

For example, log base 2 of 8: ln(8) / ln(2) = 3.

Practical Applications

• Decibels: 20 * log(V2/V1) for voltage ratio
• pH: -log(H_concentration)
• Information theory: ln(2) * bits for nats
• Compound growth: natural log for continuous compounding

Error Handling

Both log and ln require positive arguments. Attempting log(0) or ln(-1) produces a descriptive error message.