#Evaluating logs free#

#Evaluating logs free#

The pH is the negative logarithm of the concentration of free To measure the pH or acidity of a chemical solution.Intensity, and dB (decibels) are a logarithmic scale. We perceive loudness of sound as the logarithm of the actual sound To model many natural processes, particularly in living systems.Why do we use logarithms, anyway? I could write a whole articleĪbout them-maybe one day. Today, logs are no longer used in routine number crunching.īut there are still good reasons for studying them. See Eli Maor’s e: The Story of a Number for more on Was nothing more than a device built for doing various computations Once almost a cartoon trademark of a scientist, By cutting the time they spent doingĪrithmetic, logarithms effectively gave them a longer productive Back then scientists, astronomers especially, used to spend huge amounts The invention of logs in the early 1600s fueled the scientific Every decent algebra books had pages and pages of log tables at You needed logs to compute most powers and roots with fairĪccuracy even multiplying and dividing most numbers wereĮasier with logs. “student years” that’s the age of the dinosaurs-the answer Read that as “the logarithm of x in base b is theĮxponent you put on b to get x as a result.” Where Did Logs Come From? Substituting the second equation into the first to eliminate The unknown “?” is the logarithm, and 81 is theĪ logarithm is nothing more than an exponent.Ĭompactly, and show the log as an exponent, by The logarithm is 3 and the antilogarithm is In either equation, x is the antilogarithm and That inverse relationship, showing how an exponential equation is The result of raising the base to that exponent.įunction is defined as the inverse of theī x function. The logarithm is the exponent, and the antilogarithm is You don’t see the word very often, but you couldĪlso say that x is the antilogarithm of y to theīase b. Say that y is “the logarithm of x to the base b”Įvery exponential equation can be rewritten as a logarithmic equation,Īnd vice versa, just by interchanging the x and y For instance, since 5² = 25, we know that 2 (the Is just the exponent you put onto b to make the resultĮqual x. Divide Numbers, Subtract Their Logarithms.