It drives me batty because we learn the properties of logarithms before (if ever) internalizing what they mean. Here's my intuition if it helps someone: http:/

It drives me batty because we learn the properties of logarithms before (if ever) internalizing what they mean. Here's my intuition if it helps someone: http://betterexplained.com/articles/think-with-exponents/ http://betterexplained.com/articles/think-with-exponents/ Exponents let you plug in time, and get the amount of growth. e^3 ~ 20, which means "3 periods of 100% continuous growth [100% is implied by e, 3 = 3* 1] will grow us from 1 to 20". Logarithms let us plug in the growth, and get the time it took to get there. ln(20) ~ 3 means "It takes 3 units of time [growing at 100%, continuously] to grow from 1 to 20". Exponents take inputs and find the future state, logs take the future state and work backwards to find the inputs that got us there.