Proving Logarithms

christina_daae

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Nov 15, 2014
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1
Hello.
1. Prove that for all m and n, lognA = (lognA)/(lognM).
2. If a^2 + b^2 = 23ab, prove that log(a+b)/5 = (loga + logb)/2

Thank you!
 
Hello.
1. Prove that for all m and n, lognA = (lognA)/(lognM). ..............use definition of log function e.g. loga(b) = c → ac = b
2. If a^2 + b^2 = 23ab, prove that log(a+b)/5 = (loga + logb)/2 .......... a2 + b2 + 2ab = 25ab

Thank you!
.
 
Hello.
1. Prove that for all m and n, lognA = (lognA)/(lognM).
In addition to the fact that you have shown no attempt to prove this- it isn't true. You have copied the problem incorrectly. What you want to prove is that \(\displaystyle log_n(A)= \frac{log_m(A)}{log_m(n)}\) (or \(\displaystyle log_m(A)= \frac{log_n(A)}{log_n(m)}\))
Do you see the difference?

2. If a^2 + b^2 = 23ab, prove that log(a+b)/5 = (loga + logb)/2
is this supposed to be log((a+b)/5) or (log(a+ b))/5?

thank you!
 
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