![]() ![]() 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 $c=8$. Let's say I didn't tell you what the exponent $k$ was. We can use the rules of exponentiation to calculate that the result is 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 $2^3$. In other words, if we take a logarithm of a number, we undo an exponentiation. ![]()
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