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) About Me  (Show Source):
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log%28%28150%29%29=log%28%283%2A5%2A2%2A5%29%29=log%28%282%2A3%2A5%5E2%29%29

log%28%282%29%29%2Blog%28%283%29%29%2B2%2Alog%285%29%29

Substituting the given information
a%2Bb%2B2%2Alog%28%285%29%29

Answer by MathLover1(20849) About Me  (Show Source):
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log+%28%282%29%29+=+a; log%28%283%29+%29=+b+
express log%28%28150%29%29 in terms of a+and b
log%28%28150%29%29
=log%28%2825%2A6%29%29
=log%28%285%5E2%29%29+%2B+log%28%286%29%29
=2log%28%285%29%29+%2B+log%28%282%2A3%29%29
=2log%28%285%29%29+%2B+log%28%282%29%29%2Blog%28%283%29%29
=2log%28%285%29%29+%2B+a%2Bb


Answer by Alan3354(69443) About Me  (Show Source):
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if log 2 = a; log 3 = b express log 150 in terms of a and b
---------------
150 = 2*3*5*5 = 2*3*10*10/(2*2)
log(10) = 1

Answer by ikleyn(52781) About Me  (Show Source):
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.
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%2810%2F2%29 = 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) About Me  (Show Source):
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if log 2 = a; log 3 = b express log 150 in terms of a and b
matrix%281%2C3%2C+log+%28%28150%29%29%2C+%22=%22%2C+log+%28%28150%282%29%2F2%29%29%29 ----- Multiplying 150 by 2, and then DIVIDING by 2


highlight_green%28matrix%281%2C3%2C+log+%28%28150%29%29%2C+%22=%22%2C+b+%2B+2+-+a%29%29 ------- Substituting "b" for log (3), and "a" for log (2)