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3 years ago

15. Explain why we need to specify 0 1 as valid values for the base b in the expression logb(xx).

Mathematics

1 answer:

damaskus [11]3 years ago

3 0

Answer:

The base (b) has to be positive and different of 1. The logarithm is the inverse of exponential, so:

logb(a) = x ⇒ a = bˣ

So, for b = 0 ⇒ 0ˣ = a

And there is impossible, "a" only could be 0.

For b = 1 ⇒ 1ˣ = a

And the same thing would happen, the logarithming would be to be 1, and the function will be extremally restricted.

For b<0, then the expression a = bˣ will be also restricted, and will not represent all values of a.

So, 0<b<1 and b >1.

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15. Explain why we need to specify 0 < b < 1 and b > 1 as valid values for the base b in the expression logb(xx).