Students convert between exponential and logarithmic forms, interpret logarithms as exponents, and evaluate logarithms with exact integer values, including values involving 1 and negative integer exponents. Students apply the product, quotient, and power laws to expand and condense real logarithmic expressions with positive arguments, using familiar integer and rational powers while recognizing that logarithms do not distribute over sums or differences. Students solve simple logarithmic equations and exponential equations by using inverse relationships and logarithm properties, checking that bases are positive and not 1, all arguments are positive, and solutions satisfy the original equations.