Pre-cal help with probles like e^x, ln logs etc.

[austin1250]

In calc we are having like this flash card quiz and you have to apply things to the graph of like e^x or lnx.

I was wondering how do you determine the domain range of graphs like these.

for example e^x graph domain is all reals, and the range is 0 to infinity. How would you transform this graph and still determine the domain/range? would it be like 2^x and then the range just changes to 2 to infinity?


And also question about ln verse log base of 10

how would you go about like getting ln100 and find out what is that equal to of the follwing in base 10.

ex answer choices are. log e , 2/log e , log(100e), log e /2 , none of these

 

[Dick]

You really figure out domains and ranges by getting experience with graphing functions. That's about it. For example, the range of 2^x is not (2,infinity). What is it? Try graphing it. For the log_10 question, log_a(x)=log_b(x)/log_b(a). You pick a and b appropriate to the problem.

 

[Architeuthis Dux]

I can provide some insight into these questions about pre-calculus and calculus concepts. In terms of determining the domain and range of graphs like e^x, it is important to understand the properties of exponential functions. The domain of an exponential function is always all real numbers, as you mentioned. This is because the function can take any real number as an input and produce a real number as an output. The range, on the other hand, will depend on the base of the exponential function. For e^x, the base is e (approximately 2.718), which means the range will be all positive real numbers from 0 to infinity.

If you were to transform this graph by changing the base to 2, as in the example you mentioned, the range would indeed change to 2 to infinity. This is because the base of the function determines how quickly the values increase or decrease. For example, 2^x will increase much faster than e^x, leading to a larger range.

As for the question about ln and log base 10, it is important to understand that ln is the natural logarithm, which means the base is e. In comparison, log base 10 is the common logarithm, with a base of 10. To find the equivalent of ln100 in base 10, you can use the change of base formula: log base b of x = ln(x)/ln(b). In this case, b would be 10. So ln100 would be equal to log(100)/log(10) or 2/log(10). This means the correct answer choice would be 2/log e.

I hope this helps clarify these concepts for you. Remember, in mathematics, it is important to understand the fundamentals and properties of different functions to be able to solve problems and apply them to different scenarios. Keep practicing and seeking help when needed, and you will continue to improve in your understanding of these concepts.