Question

find the exact value of the expression. log base 3 of (1/27)

Answer 1

3^? = 1/27

Answer 2

first, what is the correct exponent for this equation:
3^? = 27

Answer 3

okay so it's going to be 3^3. I was just tripped up over the !/27 cause doesn't that signify a negative number or the inverse of a positive number? perhaps I'm getting my ideas mixed up in my head!

Answer 4

hmm can you expand the \(\bf log_3\cfrac{1}{27}\) ?

notice the rules -> http://www.chilimath.com/algebra/advanced/log/images/rules%20of%20exponents.gif

Answer 5

excuse my typo, 1/27!

Answer 6

@JosephineM you want the inverse 1/27 instead of 27

so instead of 3, you enter?

Answer 7

@mathessentials you would enter -3. Right?

Answer 8

yep :)

Answer 9

\(\bf a^{-n} = \cfrac{1}{a^n}\)

Answer 10

Hi, jdoe0001, thanks for the link! so when you have a log base raised to an exponent like 1/27 you form two logs separated by a subtraction sign?

Answer 11

well, no need really, what... did you get?

Answer 12

@mathesssentials thanks for the help!!

Answer 13

thought about expand it first, but then there's no actual need for that, just use the exponential version of it and that'd simplify it easy

Answer 14

@jdoe0001 Oh okay, nonetheless thank you for the chart! I'm positive that it will come in handy if I encounter some really nasty log problems!

Answer 15

yw