MHB What conclusions can we draw about c in the logarithmic properties of a and b?

AI Thread Summary
The discussion centers on the logarithmic equation $$\log_{b}(a) = c$$ with the constraints that 0 < a < 1 and b > 1. It is concluded that c must be negative because the logarithm of a number less than 1 (in this case, a) with a base greater than 1 (b) yields a negative result. The participants emphasize the importance of showing progress in problem-solving to facilitate better assistance. The conversation encourages users to share their thought processes to avoid redundant suggestions from helpers. Overall, the key takeaway is the relationship between the values of a, b, and c in logarithmic properties.
cherikana
Messages
1
Reaction score
0
$$\log_{b}\left({a}\right) =c ,0<a<1<b$$
What can you conclude about c? explain.
 
Last edited by a moderator:
Mathematics news on Phys.org
cherikana said:
$$\log_{b}\left({a}\right) =c ,0<a<1<b$$
What can you conclude about c? explain.

Hi cherikana! Welcome to MHB! (Smile)

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »

Similar threads

B Characteristics of the parent logarithmic function
Replies
4
Views
2K
MHB How Can I Express a Combination of Logarithms as a Single Logarithm?
Replies
3
Views
2K
MHB Triangle and logarithm problem
Replies
5
Views
2K
B Commutative & Associative property of negative numbers
Replies
4
Views
3K
I Question about branch of logarithms
Replies
14
Views
3K
B Issue With Algebra of Logarithms
Replies
8
Views
1K
MHB Help with Logarithms: Find 2^A
Replies
2
Views
2K
MHB Find Product: $(a^4+b^4+c^4)$ and $(a^6+b^6+c^6)$
Replies
3
Views
1K
Using Properties of Logarithms
Replies
22
Views
3K
MHB 411.1.3.15 Prove A\cap(B/C)=(A\cap B)/(A\cap C)
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top