Can Logarithmic Functions Be Zero or Negative?

  • Thread starter Byrgg
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    Logarithms
In summary, the conversation discusses a question about the range and domain of the function y = b^n and the possibility of log(b) n being negative or 0. The person asking the question is in grade 11 and looking at a grade 12 textbook, and they are unsure if this is the appropriate place to post their question. They also mention wanting an explanation rather than just a one-word answer. Another person responds with some information, but admits it may not be correct and suggests that the domain for log(b) n is x>0 based on calculator results.
  • #1
Byrgg
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I'm only in gr.11 right now, and I was looking at a gr.12 textbook, since this isn't really homework I decided to post this here, is that ok or is this the wrong board?

Well anyway, it asked what the range of of the function y = b ^ n would be (and the domain) and also if log(b) n could ever be negative or 0.

Could someone please help?
 
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  • #2
Err, a correction quickly, it asks the range of y = b^ n and what that means for the domain of log(b) n, it still asks if log(b) n can ever be 0 or negative though.
 
  • #3
Oh and an explained answer(not just a one word one) is hoped for.
 
  • #4
Byrgg said:
Err, a correction quickly, it asks the range of y = b^ n and what that means for the domain of log(b) n, it still asks if log(b) n can ever be 0 or negative though.
ur question is really confusing I am doing yr 12 and started log about 2 weeks ago. but i can giv u some infos . it may not b correct lol.
if u type in calculator log0 or ln0 u get an MA error. so yeh the domain is x>0
 

What are logarithms and why are they useful?

Logarithms are mathematical functions that represent the inverse of exponential functions. They are useful because they allow us to solve complex exponential equations by simplifying them into linear equations.

How do you solve logarithmic equations?

To solve logarithmic equations, you can use the properties of logarithms, such as the product, quotient, and power rules. You can also use the fact that logarithms are the inverse of exponentials to rewrite the equation in exponential form and solve for the variable.

What is the difference between natural logarithms and common logarithms?

Natural logarithms, or ln, use the base e (approximately 2.718) while common logarithms, or log, use the base 10. Natural logarithms are often used in calculus and other advanced mathematics, while common logarithms are used more in everyday calculations.

How can logarithms be applied in real life?

Logarithms have many applications in real life, such as in finance, population growth, and chemistry. For example, they can be used to calculate compound interest, model population growth, and measure the pH of a solution.

What is the relationship between logarithms and exponential growth?

Logarithms and exponential growth are inversely related. This means that as the base of the logarithm increases, the rate of exponential growth decreases. This relationship is important in understanding the growth and decay of various phenomena in science and economics.

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