Logarithms

• How to Solve $8n^2=64n\log_2(n)$
  Divide by 8n to reduce the equation to n = 8 log base 2 of n; it has two positive real solutions, approximately 1.1000 and 43.5593.
• How to Convert an Exponential Expression to a Different Base
  Rewrite an exponential expression from base a to base b using logarithms: a^x = b^(x log_b a), with examples and domain conditions.
• How to Calculate a Logarithm Without a Calculator
  Use logarithm laws for exact values, estimate by powers and familiar logs, or apply a convergent series to calculate logarithms by hand.
• How to Find an Antilog on a Simple Calculator
  To find a common antilog, enter the exponent into 10^x, often SHIFT or 2nd plus LOG. For another base, calculate that base to the exponent.
• How to Find the Inverse of a Sigmoid Equation
  Invert the standard logistic sigmoid by taking the log-odds: x = ln(y/(1−y)). This guide derives the formula, its domain, and scaled variants.
• How to Solve the Continuous Compounding Formula for r
  Rearrange the continuous-compounding equation A = Pe^(rt) with a natural logarithm to find the rate r from principal, final amount, and elapsed time.