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?
 

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