Apply exponent and logarithm laws to simplify, expand, and condense expressions, including zero, negative, and rational exponents where defined, and convert accurately between exponential and logarithmic forms while respecting domain restrictions. Graph and interpret transformed exponential and logarithmic functions, identifying growth or decay, asymptotes, domain, range, intercepts, transformations, and parameters in models such as $y=ab^x$, $y=Ae^{kx}$, and $y=a+b\log_c(x-h)$. Model exponential growth and decay and solve exponential equations using common bases or logarithms, as well as logarithmic equations, verifying solutions and rejecting those that violate positivity or introduce extraneous values.