Multiplying two logarithms (Solved) - Mathematics Stack Exchange I was wondering how one would multiply two logarithms together? Say, for example, that I had: $$\log x·\log 2x < 0$$ How would one solve this? And if it weren't possible, what would its domain be? Thank you! (I've uselessly tried to sum the logs together but that obviously wouldn't work Was just curious as to what it would give me)
What is the point of logarithms? How are they used? [closed] Logarithms are a convenient way to express large numbers (The base-10 logarithm of a number is roughly the number of digits in that number, for example ) Slide rules work because adding and subtracting logarithms is equivalent to multiplication and division (This benefit is slightly less important today ) Lots of things "decay logarithmically"
logarithms - What is the reason to introduce and study logarithmic . . . Logarithms were originally invented to make multiplication (as in, actually computing the product of two numbers by hand) easier They were developed by one man, John Napier, in the 16th century, specifically as a method for doing by-hand multiplication
logarithms - The difference between log and ln - Mathematics Stack Exchange In the early '70s, calculators became widespread Before then, many books had tables of base-$10$ logarithms in an appendix Suppose you wanted the logarithm of $123$ The table gave you logarithms of numbers between $1$ and $10$, so you found $\log_{10}1 23= 0 089905\ldots$ and concluded that $\log_{10} 123 = 2 089905\ldots\;{}$
Calculate logarithms by hand - Mathematics Stack Exchange You could build a table of certain logarithms: 10^(-1 2), 10^(-1 4), etc Twenty such entries would allow you to calculate logs to 5 places by multiplying your target number by the appropriate power of ten and adding the negative of that log to the total You could probably use two soroban: one for the division, and one to accumulate the log
Easy way to compute logarithms without a calculator? See the HHC 2018 proceedings for a paper on the computation of logarithms Generally, power series are efficient for natural logarithms of numbers near $1$ You can do things to get your number near $1$, such as multiplying by a power of ten or taking the square root, then adjusting the logarithm you get Meanwhile, memorize the number $0 4343$