Question 1203523: Hello everyone, I am doing some problems on logarithms but was struggling with a couple of them. I will post them one at a time like the rules mandate.
Suppose that x=ln(A) and y=ln(B). Write the following expression in terms of x and y (so there won't be an A or B).
ln(A^5 * squareroot B)=?
Found 3 solutions by MathLover1, ikleyn, josgarithmetic:
Answer by MathLover1(20850)   (Show Source):
Answer by ikleyn(52884)  (Show Source):
You can put this solution on YOUR website! .
Hello everyone, I am doing some problems on logarithms but was struggling with a couple of them.
I will post them one at a time like the rules mandate.
Suppose that x=ln(A) and y=ln(B). Write the following expression in terms of x and y (so there won't be an A or B).
ln(A^5 * squareroot B)=?
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They want you learn and use the basic rules of logarithms
ln(p*q) = ln(p) + ln(q),
ln(p^n) = n*ln(p).
It is true not only for the natural logarithms, but for any other logarithm bases, too.
So, in this case, the solution is in one single line
 =  +  = 5*ln(A) +  = 5x +  y. ANSWER
Solved.
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There is no any need to make writing longer.
Some tutors at this forum think that the longer their writing is - the better their solutions look like
- the smarter they are looking, themselves.
Although in Math, everything is exactly in reversed order - nothing in writing should be longer than it should be.
Only because of it, Math is beautiful as an art,
and is not so terrible as a swamp.
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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.
Answer by josgarithmetic(39630)  (Show Source):
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