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

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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
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$$\log_{b}\left({a}\right) =c ,0<a<1<b$$
What can you conclude about c? explain.
 
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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?
 
I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...

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