SOLUTION: prove the power property: log<sub>b</sub>U<sup>n</sup> = n·log<sub>b</sub>U

Algebra.Com
Question 82835: prove the power property: logbUn = n·logbU
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!

prove the power property: logbUn = n·logbU

Proof is by induction:

First we prove it's true for n = 1.

logbU1 = logbU = 1·logbU

Assume true for n < k,

Need to prove that logbUk+1 = (k+1)logbU

logbUk+1 = logb(UkU1) = logbUk + logbU1

= k·logbU + logbU =  (logbU)(k+1) = (k+1)logbU

Edwin
RELATED QUESTIONS

log34xlog34x =... (answered by chitra)
What is: 3log3x + 4logx - 12 log-4/3x? (answered by Edwin McCravy)
prove that logam = logbm ×... (answered by karaoz)
Solve for x
(log3x)2 + log3x2 + 1 =... (answered by Edwin McCravy)

When the constraint 6x1 + 17x2 < 28 is converted to an... (answered by Edwin McCravy)

Find the logarithm using the change of base formula:
Log3(13)       formula... (answered by AnlytcPhil)


I need the answer for question (i) and (ii) both of them please:

(2) Let... (answered by Edwin McCravy,AnlytcPhil,ikleyn)

If loga(m) = p and logb(m) = q (a&b are bases) 
prove that... (answered by Edwin McCravy)

Let logbA = 2.487 and logbB = 0.392. Find... (answered by kapilsinghi)