Question

Last question!!!
log 1/5 (25)

Answer 1

check the identity by evaluating...

Answer 2

\[\huge \log_{\frac{ 1 }{ 5 }}25 \]

Answer 3

use the same property i gave for last Q

Answer 4

\(\frac{1}{5} = 5^{-1}\). What would you multiply to that to get \(5^2\)?

Answer 5

yes, simplify numerator and denominator separately.

Answer 6

\[\large \log_{\frac{ 1 }{ 5 }} 5 = \frac{ \log_{5} 25 }{ \log_{5}\frac{ 1 }{ 5}} = \frac{ \log_{5} 5^2 }{ \log_{5} 5^{-1}}\]

Answer 7

Why so serious?

Answer 8

Just figure out what you multiply to \(5^{-1}\) to get \(5^2.\)

Answer 9

ahh @agent0smith explained it pretty good :)

Answer 10

@agent0smith
How did you get the base to be 5? Like all of them?

Answer 11

Not sure what you mean... I just used base 5 because it makes it easy to solve.

Answer 12

@AonZ Change of bases.

Answer 13

you can choose any base for using that property,e,5,10,... thats why its unspecified in the property

Answer 14

so if you use change of base rule you can choose ANY base?

Answer 15

Yes.

Answer 16

wow i reckon i understand logs a lot better now :P

Answer 17

^ correct

@ParthKohli shouldn't it be "figure out what power you need to raise 5^-1 to, to get 25" as opposed to "Just figure out what you multiply to 5^−1 to get 5^2"?

Answer 18

Yes, I am sorry.

Answer 19

But you get the point.

Answer 20

Ah okay, cos i was wondering how this helps:\[5^{-1} \times 5^3 = 25\]compared to this
\[(5^{-1})^{-2}=25\]

Answer 21

:-)