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)
            
        1/2log base 4 25-2(3logbase4 5-log base 4 25)
Answers
                    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
    
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
    
= 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 :
    
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
    
-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.
    
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
    
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!!!!
    
...-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)
    
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
    
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