Kenneth S. answered • 07/14/16
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a) 52log53
Simplify the exponent: log532
This exponent is log59
Now when you put this in exponent land, with base 5, the exponentiation (base 5) and the log-taking (base 5) cancel out one another, leaving the answer NINE.
Are you making any progress in understanding? Remember: LOGARITHMS ARE EXPONENTS, and the dual acts of exponentiating to a logarithm, when you have base agreement, gives you just the argument (9, in this case).
This is an instance of f(f-1(x)) = x. Recall that the graphs of ln x and ex are reflections of one another in the line y=x, which means that exp(x) and ln(x) are inverses of one another.
To do logs/exponents well, you must study until you get the necessary depth of understanding. Read the textbook; look at Kahn Academy for help. Good luck.
Kenneth S.
Thank you, Alex. If it's not too much trouble, I would like you to describe what textbook(s) are in use in your class.
I ask this because I am finding that many schools around the nation have put aside proven, perfected textbooks of the past, substituting Johnny-come-lately materials created by for-profit outfits, in response to the Common Core stampede. I am collecting anecdotes, articles, etc. (often found on the internet) about the Common Core fiasco--I say fiasco because the fault of poor performance in mathematics is not in the former material, but in the society itself that has not taught the values of study, dedication, learning to the youth of the nation, and has underfunded schools and overloaded teachers will excessive dictates.
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07/14/16
Alex C.
I agree completely. The book Im currently using was actually written by a former teacher in my school. Its not sold to the public. If a student is taking the math I am in, then they have to go to the school bookstore and buy it.
My current teacher told us he didn't like the way the book was written . The sequence of the topics is just all over the place.
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07/16/16
Kenneth S.
Thanks, Alex...I appreciate the time to answer my inquiry. One thing that just occurred to me is that you might go to OPAMP bookstore in Hollywood and purchase a used Algebra II textbook (if that store is still in business). Or go online for used math books.
Encourage your teacher to teach his way, addressing topics in the most natural way--rather than following in lockstep with a poorly organized textbook. A good teacher lectures a lot (in a Socratic way, i.e. blending in questions to get student participation) so that everyone understands not only WHAT, but WHY.
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07/16/16
Alex C.
07/14/16