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1/2 Log r + 1/3 log s - 1/4 log t

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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L = 1/2 log r + 1/3 log s - 1/4 log t
 
Use Power Rule of Logarithms:
 
L = log(r^(1/2)) + log(s^(1/3)) - log(t^(1/4))
 
Use Multiplication Rule of Logarithms:
 
L = log( (r^(1/2)) * (s^(1/3)) ) - log(t^(1/4))
 
Use Quotient Rule of Logarithms:
 
L = log( ( (r^(1/2)) * (s^(1/3)) ) / (t^(1/4)) )
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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The question is combine all log terms as one log
 
    We make use of properties of log function:
 
       log AB = log A + lobB
 
         A = ab      b = log aA
 
 
      1/2 log r + 1/3 logS - 1/4 log t 
 
          log (√r . 3√s) / 4√t ) = log 24√( r12 . S8/  t6 )
 
 
       Note that    a1/n n√a
 
                        n√a . m√b  = mn√ (an . bm )        
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
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Hi Juan;
I do not know what you are trying to do.  I will do my best...
1/2 Log r + 1/3 log s - 1/4 log t
Let's apply the principle of...
log xy=y log x
log r1/2+log s1/3-log t1/4
Let's apply the principle of...
log ab=log a + log b
log (r1/2)(s1/3)-log t1/4
Let's apply the principle of...
log a/b=log a - log b
log[(r1/2)(s1/3)]/(t1/4)