SOLUTION: Express in terms of sums and differences of logarithms {{{log((5a/(4b^2)))}}} Write in simplest radical form: {{{root(3,5x^5)}}}

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Question 145816: Express in terms of sums and differences of logarithms

Write in simplest radical form:

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Express in terms of sums and differences of logarithms
log(5a/4b^2) = log(5a) - log(4b^2)
= log5 + loga - log4 - 2logb
--------------------------

1n small 3 on top of sqrt sign 5x^5
(5x^5)^(1/3)
= x*(5x^2)
==============
Cheers,
Stan H.

Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
Express in terms of sums and differences of logarithms


Use this rule:----------- 



Use this rule:-----------    
on both terms above being very careful to put the
results of the second term in parentheses because
it has a minus sign in front of it, which will 
change the signs:


 
Now remove the prentheses:



Use this rule:----------- 
on the last term:



-----------------------------------------------------

Write in simplest radical form:


Write that as



The index is 3 (cube root),
we make as many groups of three like factors
as we can and leave the others ungrouped, like
this:



We were only able to make one group in this
problem but in other problems you can make more
groups.

The TRIPLE  comes out in front as a 
SINGLE  and the other factors stay underneath
the radical:



Then you write the {{(x*x}}} under the radical as 



------------------------------
Edwin


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