SOLUTION: If log base b of 2 =x and log base b of 3 = y, evaluate the following terms of x and y: A) log base b of 36 B) log base b of 432 C) log base b of 3 (all over) log base b

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If log base b of 2 =x and log base b of 3 = y, evaluate the following terms of x and y: A) log base b of 36 B) log base b of 432 C) log base b of 3 (all over) log base b      Log On


   

Question 1143776: If log base b of 2 =x and log base b of 3 = y, evaluate the following terms of x and y:
A) log base b of 36
B) log base b of 432
C) log base b of 3 (all over)
log base b of 4
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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(A)  36 = 4*9 = 2%5E2%2A3%5E2.


     Therefore,  log%28b%2C%2836%29%29 = log%28b%2C%284%2A9%29%29 = log%28b%2C%284%29%29 + log%28b%2C%289%29%29 = log%28b%2C%282%5E2%29%29 + log%28b%2C%283%5E2%29%29 = 2%2Alog%28b%2C%282%29%29 + 2%2Alog%28b%2C%283%29%29 = 2x + 2y.     ANSWER




(B)  432 = 16*27 = 2%5E4%2A3%5E3.


     Therefore,  log%28b%2C%28432%29%29 = log%28b%2C%2816%2A27%29%29 = log%28b%2C%2816%29%29 + log%28b%2C%2827%29%29 = log%28b%2C%282%5E4%29%29 + log%28b%2C%283%5E3%29%29 = 4%2Alog%28b%2C%282%29%29 + 3%2Alog%28b%2C%283%29%29 = 4x + 3y.     ANSER



(C)  log%28b%2C%283%29%29%2Flog%28b%2C%284%29%29 = y%2F%282x%29.      ANSWER

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On logarithms and their properties,  see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.