can someone please show me step by step how to do this problem...

Question

1/2log base 4 25-2(3logbase4 5-log base 4 25)

Answer 1

.5 log4 5^2 = log4(5)

2(3 log4 5 - 2 log4 5 ) = 2 log4 5
so we have
-1 log4(5)
= log4(.2)

that might be the answer you are looking for but if you need a number
4^x = .2 ?
x ln 4 = ln .2
x = 1.39/-1.61
= - .863

Answer 2

1/2log base 4 25-2(3logbase4 5-log base 4 25)
= 1/2 log₄ 25 - 2(3log₄ 5 - log₄ 25)
= log₄5 - 2(log₄125 - log₄25)
= log₄5 - 2(log₄(125/25)
= log₄5 - 2log₄5
= -log₄5

Answer 3

I have to condense it... thanks for your help

Answer 4

my teacher has a different answer... she has log base 4(1/25).

Answer 5

Well, I think log4 (1/5)
I got -1 log4 5
she got -2 log4 5
one of us subtracted wrong or something
However Reiny and I agree exactly, so the odds are in our favor :

Answer 6

my teacher got log base 4 (1/125) and it's a quiz review sheet, and all the math teachers look over it... sooo... I get how to simplify the 1/2 part but how do i condense the parenthesies

Answer 7

By the way, your teacher and I both said
-n log4 x = log4 x^-n = log4 (1/x^n)
which is how we converted the negative log to positive

Answer 8

can you please show me how to condense -2(3logbase 4 5-log base 4 5), thanks:)

Answer 9

Well, Miley, if you typed your question correctly, then your teacher is wrong.

Even though both Damon and I did it slightly differently, we came up with the same answer.

I evaluated your original expression the way it stands on my calculator, and got the same result as our answer at the end.

Answer 10

I do not know what to say. Reiny and I did the parentheses quite different ways and both got the same answer.

Answer 11

Can you please break it down step by step and show me how you did it! thanks:)

Answer 12

You have two ways to condense the inside the parentheses up there

I did it by saying log 25 = 2 log 5

Reiny did it by saying
log 125 - log 25 = log (125/25) = log 5

Answer 13

what happen to the base 4?

Answer 14

OK, Miley, in your first post you had

...-2(3logbase4 5-log base 4 25)

and now you typed
...-2(3logbase4 5-log base 4 5)

GheeeeZZ!!!!

Answer 15

-2(3logbase 4 5-log base 4 5)
Hey, that is not what you wrote in the original question
that is just -2 (2 log4 5)
which is
-4 log4 of 5

NOW
log4 5 - 4 log4 5
= -3 log4 5
= log4 (1/5^3)
= log4 (1/125)

Answer 16

What I wrote a few minutes ago is true for any old base so I left the 4 out

Answer 17

oh my bad, sorry. wait how did you get rid of the negative two on the outside?

Answer 18

ohh okay thanks

Answer 19

-2(2 log) = -4 log

Answer 20

Sorry it's not like i did that on purpose! Take a CHILL PILL!

Answer 21

huh??

Answer 22

Uh...I'm posting this one on gothomework.tk