Question

log 1/9 base 81

Answer 1

let me give you a hint, 1/9 = 9 to the power of -1, 81 = 9^2

Answer 2

And remember, \(\Large \log_{b}x=y \) means that \(\Large b^y=x \)

...that is, y is the POWER to which you take the BASE b to produce the RESULT x. :)

Answer 3

wanna know how to cheat using a calculator? it is easy

Answer 4

your math teacher wants you to solve
\[\left(\frac{1}{9}\right)^x=81\]which is not really that hard, because
\[\left(\frac{1}{9}\right)^{-1}=9\] and so
\[\left(\frac{1}{9}\right)^{-2}=81\]

Answer 5

but if you don't feel like doing all this thinking, then whip out the calculator and compute
\[\frac{\log(81)}{\log(\frac{1}{9})}\]

Answer 6

you should get \(-2\) in a flash

Answer 7

http://www.wolframalpha.com/input/?i=log%2881%29%2Flog%281%2F9%29

Answer 8

*cough cough*.... I feel compelled to point out that THIS math teacher would want to make sure that you understand the concept of the log function and how it relates to exponential functions.

And while it's true that the handy calculator "trick" above will work (not really a trick of course, just change of base formula)..... this is EXACTLY the kind of problem that I, being all old-school and stuff as I am, might put on a quiz or test that I'm giving WITHOUT allowing the use of calculators. Yeah, I'm like that. :)