Understanding Logarithmic Properties: Explained with Examples

AI Thread Summary
The discussion clarifies the logarithmic property that states log base c of a raised to b equals b times log base c of a. The initial confusion arose from misapplying the formula, leading to incorrect calculations. The correct expression is log_c(a^b) = b * log_c(a), which can be proven using exponential properties. Participants emphasize the importance of understanding the relationship between logarithms and exponents. This clarification helps resolve discrepancies in calculations involving logarithmic expressions.
Rafe
Messages
2
Reaction score
0
Okay i did a search for logarithmic properties and logarithms and couldn't seem to find an explanation for how this particular property works.
(log base c of a ) ^ b = b (log base c of a)
when i input simple numbers like :
PHP:
a=4
b=3
c=2
Log base 2 of 4 obvioussly the answer is 2, but
2^3 /= (does not equel) 3 x 2.
i dont' know how to make sense of this discrepency. i imagine I'm just reading it wrong.
 
Physics news on Phys.org
hmmm the right formula is log_c(a)^b=blog_c(a)

edit: heh, I am tired =P
 
Last edited:
because (c^a)^b=c^{a*b}.
 
Last edited:
Actually the correct formula is:

\log_c(a^b) = b\log_c (a)

This can be proven by taking the base c exponential of each side:

c^{\log_c(a^b)} = a^b

c^{b\log_c (a)} = (c^{\log_c (a)})^b= (a)^b
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
Back
Top