SOLUTION: if log 2 = a; log 3 = b express log 150 in terms of a and b

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Question 1184865: if log 2 = a; log 3 = b express log 150 in terms of a and b
Found 5 solutions by josgarithmetic, MathLover1, Alan3354, ikleyn, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!




Substituting the given information
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

;
express in terms of and

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Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
if log 2 = a; log 3 = b express log 150 in terms of a and b
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150 = 2*3*5*5 = 2*3*10*10/(2*2)
log(10) = 1

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
if log 2 = a; log 3 = b express log 150 in terms of a and b
~~~~~~~~~~~~~~~~ 

If log(2) = a  and  log(3) = b are given,  then   log(5) =  = log(10) - log(2) = 1 - a
we also can consider as given value.



THEREFORE,  log(150) = log(25*6) = log(5^2) + log(2) + log(3) = 2*log(5) + log(2) + log(3) = 2*(1-a) + a + b = 2 - 2a + a + b = 2 - a + b.    ANSWER

Solved.

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On logarithms and their properties,  see these introductory lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Evaluate logarithms without using a calculator (*)
    - Simplifying expressions with logarithms
    - Solving logarithmic equations
in this site; especially the lesson marked (*) in the list.

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.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

if log 2 = a; log 3 = b express log 150 in terms of a and b
 ----- Multiplying 150 by 2, and then DIVIDING by 2


 ------- Substituting "b" for log (3), and "a" for log (2) 

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