Asked by Miley

can someone please show me step by step how to do this problem...
1/2log base 4 25-2(3logbase4 5-log base 4 25)
Answered by Damon
.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
Answered by Reiny
1/2log base 4 25-2(3logbase4 5-log base 4 25)
= 1/2 log<sub>4</sub> 25 - 2(3log<sub>4</sub> 5 - log<sub>4</sub> 25)
= log<sub>4</sub>5 - 2(log<sub>4</sub>125 - log<sub>4</sub>25)
= log<sub>4</sub>5 - 2(log<sub>4</sub>(125/25)
= log<sub>4</sub>5 - 2log<sub>4</sub>5
= -log<sub>4</sub>5
Answered by Miley
I have to condense it... thanks for your help
Answered by Miley
my teacher has a different answer... she has log base 4(1/25).
Answered by Damon
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 :
Answered by Miley
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
Answered by Damon
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
Answered by Miley
can you please show me how to condense -2(3logbase 4 5-log base 4 5), thanks:)
Answered by Reiny
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.
Answered by Damon
I do not know what to say. Reiny and I did the parentheses quite different ways and both got the same answer.
Answered by Miley
Can you please break it down step by step and show me how you did it! thanks:)
Answered by Damon
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
Answered by Miley
what happen to the base 4?
Answered by Reiny
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 <b>5</b>)


GheeeeZZ!!!!
Answered by Damon
-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)
Answered by Damon
What I wrote a few minutes ago is true for any old base so I left the 4 out
Answered by Miley
oh my bad, sorry. wait how did you get rid of the negative two on the outside?
Answered by Miley
ohh okay thanks
Answered by Damon
-2(2 log) = -4 log
Answered by Miley
Sorry it's not like i did that on purpose! Take a CHILL PILL!
Answered by Miley
huh??
Answered by aleah
Uh...I'm posting this one on gothomework.tk