The rule for the log of a reciprocal follows from the rule for the power of negative oneĪnd the above rule for the log of a power. But that can be done an easier way: 5-3 could also be calculated like: 1 ÷ (5 × 5 × 5) 1/53 1/125 0.008. The logarithm with base $b$ is defined so thatįor any given number $c$ and any base $b$.įor example, since we can calculate that $10^3=1000$, we know that $\log_ to conclude that Just like we can change the base $b$ for the exponential function, we can also change the base $b$ for the logarithmic function. Exponents With Zero Powers Any number or variable raised to the. To get all answers for the above problems, we just need to give the logarithm the exponentiation result $c$ and it will give the right exponent $k$ of $2$. In other words, the logarithm gives the exponent as the output if you give it the exponentiation result as the input. Log base 2 is defined so thatįor any given number $c$. We define one type of logarithm (called “log base 2” and denoted $\log_2$) to be the solution to the problems I just asked. But, what if I changed my mind, and told you that the result of the exponentiation was $c=4$, so you need to solve $2^k=4$? Or, I could have said the result was $c=16$ (solve $2^k=16$) or $c=1$ (solve $2^k=1$).Ī logarithm is a function that does all this work for you. To calculate the exponent $k$, you need to solveįrom the above calculation, we already know that $k=3$. Instead, I told that the base was $b=2$ and the final result of the exponentiation was $c=8$. Find more Dates & Times widgets in WolframAlpha. Let's say I didn't tell you what the exponent $k$ was. Get the free 'zero and negative exponents' widget for your website, blog, Wordpress, Blogger, or iGoogle. We can use the rules of exponentiation to calculate that the result is A beautiful, free online scientific calculator with advanced features for evaluating percentages, fractions, exponential functions, logarithms, trigonometry, statistics, and more. The result is some number, we'll call it $c$, defined by $2^3=c$. If we take the base $b=2$ and raise it to the power of $k=3$, we have the expression $2^3$. Get step by step solutions to your math problems. In other words, if we take a logarithm of a number, we undo an exponentiation. Make math easy with our math problem solver tool and calculator.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |