We are often reminded that in mathematics, no concept is simple and every concept should be taking seriously. In this unit 5 learning journal, my concentration would be on Exponential and Logarithmic Functions.
In section 1, we are told that among all the functions we have examine so far in this course, the exponential and logarithmic functions are the very ones that mostly impact our daily lives the most (Yakir, 2011). In previous learning, we dealt with various functions which includes terms like x2 or x2=3, that is, terms of the form xp where the base of the term, x, varies but the exponent of each term, p, remains constant. However, in this chapter and unit, we are exploring functions of the form f(x) = bx where the base b is a constant …show more content…
It is my understanding that logs is defined as the inverses of exponential functions; therefore, we can essential use Theorems to inform our understanding. The fact that the domain of a log function is the range of an exponential function, and that the range of a log function is the domain of an exponential function was very difficult for me to understand because similar concepts were dealt with in previous sections. However, this is a combination of two functions; the common logarithm of a real number and the natural logarithm of a real …show more content…
The major learning objective we learned here is the ability to generate and develop techniques for solving equations involving exponential functions. The one-to-one property of exponential functions informs us that 2x = 2 rise to power 7 if and only if x = 7. It therefore, indicates that not only is x = 7 a solution to 2x = 2 rise to power 7; it is, however, the real solution. There are several solutions and problem that articulate how to handle the exponential equations and inequalities. One of such steps in solving this problem is to isolate the exponential function and secondly by taking the natural log of both sides of the equation and use the Power
In section 1, we are told that among all the functions we have examine so far in this course, the exponential and logarithmic functions are the very ones that mostly impact our daily lives the most (Yakir, 2011). In previous learning, we dealt with various functions which includes terms like x2 or x2=3, that is, terms of the form xp where the base of the term, x, varies but the exponent of each term, p, remains constant. However, in this chapter and unit, we are exploring functions of the form f(x) = bx where the base b is a constant …show more content…
It is my understanding that logs is defined as the inverses of exponential functions; therefore, we can essential use Theorems to inform our understanding. The fact that the domain of a log function is the range of an exponential function, and that the range of a log function is the domain of an exponential function was very difficult for me to understand because similar concepts were dealt with in previous sections. However, this is a combination of two functions; the common logarithm of a real number and the natural logarithm of a real …show more content…
The major learning objective we learned here is the ability to generate and develop techniques for solving equations involving exponential functions. The one-to-one property of exponential functions informs us that 2x = 2 rise to power 7 if and only if x = 7. It therefore, indicates that not only is x = 7 a solution to 2x = 2 rise to power 7; it is, however, the real solution. There are several solutions and problem that articulate how to handle the exponential equations and inequalities. One of such steps in solving this problem is to isolate the exponential function and secondly by taking the natural log of both sides of the equation and use the Power