SOLUTION: Please help me with this. log7 10=X, log7 12=Y, log7 11=Z, Find log7 33/25=? Thank you.

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Question 1144036: Please help me with this.
log7 10=X, log7 12=Y, log7 11=Z, Find log7 33/25=?
Thank you.
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.

33%2F25 = %283%2A11%29%2F25 = %283%2A4%2A11%29%2F%284%2A25%29    <<<---=== I multiplied the numerator and denominator 
                                  by the factor 4, without changing the fraction.

                                  So, I can continue the chain of equalities:


33%2F25 = %283%2A11%29%2F25 = %283%2A4%2A11%29%2F%284%2A25%29 = %2812%2A11%29%2F10%5E2.


Therefore,


log%287%2C%2833%2F25%29%29 = log%287%2C%28%2812%2A11%29%2F10%5E2%29%29 = apply the logarithm properties = log%287%2C%2812%29%29 + log%287%2C%2811%29%29 - 2%2Alog%287%2C%2810%29%29 = Y + Z - 2X.    ANSWER

Answered,  explained,  solved and completed.

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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
    - Evaluate logarithms without using a calculator (*)
    - Proving equalities with logarithms
in this site.

Especially,  look into the lesson  (*)  and find there very similar solved problems.

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.