Posted by Jus on Monday, May 25, 2009 at 5:38pm.
1. Given the product law of logarithms, prove the product law of exponents.
2. Given the quotient law of logarithms, prove the quotient law of exponents.
3. Apply algebraic reasoning to show that
a=b^(loga/logb) for any a,b>0
Please explain these to me.
All I know is that
The product law of logs are:
Log(AB)=logA+logB
The Quotient law of logs are:
Log(A/B)=logALogb

Math  Reiny, Monday, May 25, 2009 at 5:55pm
1.
let a^x =m and a^y = n
by definition:
a^x = m <> log _{a} m = x and
a^y = n <> log _{a} n = y
just for the fun of it, I am going to add the two equations on the right ...
log _{a} m + log _{a} n = x+y
or log _{a} mn = x+y, since we are supposed to know the product rule of logs
but that can be changed to
a^(x+y) = mn
but what was m and n ??
so (a^x)(a^y) = mn = a^(x+y)
which is "product law of exponents"
Q.E.D.

Math  Jus, Monday, May 25, 2009 at 6:18pm
thank you
could you help me with part 3 too?
I know that part two is the same as part one except you divide. please help with part 3, thank you in advance reiny

Math  Reiny, Monday, May 25, 2009 at 6:29pm
one of the log rules states
log _{b} a = loga/logb ...(base 10, or any other legal base you want to choose)
so again by definition of the log notation
a=b^(loga/logb) for any a,b>0
<> log _{b} a = loga/logb
well, well, that was even easier than the first one.
let's test it
let a = 8 and b=2
we know log _{2} 8 = 3
and log8/log2 = .903089987/.301029995 = 3

Math  Nora Escobedo, Tuesday, October 11, 2011 at 2:01am
Which expression eqivalent to 27x^2y^6/3x^5y^2z^9?
Answer This Question
Related Questions
 Math  Given the product law of logarithms, prove the law of exponents. Given ...
 trigonometry  Use logarithms and the law of tangents to solve the triangle ABC...
 math  use the power law of logarithms to verify the product law of logarithms ...
 trigonometry  Use logarithms and the law of tangents to solve the triangle ABC...
 Math  Can the product law of logarithms be used to evaluate log(2) + log(3)? ...
 math  whats the product of 8x^2y and2xy^3? use law of exponents to find the ...
 pre cal  Approximate the following logarithms using the properties of ...
 Intermediate Algebra  Express as a sum, difference, and product of logarithms, ...
 Maths Help  (1) Prove that the cancellation law of multiplication is equivalent...
 trigonometry (repost) Mathmate  I want to start by saying thank you . You have ...
More Related Questions