logarithmic graph function

Posted: August 27th, 2021

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Week 13 Discussion

A logarithmic graph function is an equation of the form that reads y equals to the log of x, base “b” or y equals the logbase “b” ofx. In all these two equation forms, xand b are higher than zero while b is not equal to one (Makgakga and Sepang 78). On the other hand, an exponential graph relates to an exponent variable as 10 raised to power x. An exponential graph can be expressed approximately by an exponential function (Makgakga and Sepang 78). Likewise, it is well described by an exceptionally rapidly increasing exponential growth rate, either in size or extent.

The association between the graphs of exponential and logarithmic functions is illustrated in the following ways. The graphs of these two functions are not the same. Specifically, the logarithmic graph function is the inverse function of an exponential graph function. Therefore, it implies thata^x = b is an exponential graph function, whereas log base a (b) = xis a logarithmic graph function (Makgakga and Sepang 81). Their operations are inverses of one another in the sense that a person can regard the actual logarithm as the isolating variable of interest and vice versa when expressing an exponential function.

Moreover, the inverse of a logarithmic graph function is a function of an exponential graph equation. The inverse of an equation is derived by switching the x and y coordinates so that the graph reflects the line y=x(HELM 4).For instance, the actual exponential function is dictated by y = f(x) = ex while the actual logarithmic graph function is expressed as f(x) = loge x = lnx(HELM 4). In short, x is considered greater than zero. In summary, the graph function to the right-hand side of the logarithmic graph curve is a literal reflection of the exponential graph curve.

Works Cited

Helping Engineers Learn Mathematics (HELM). “Exponential and Logarithmic Functions.” Workbook 6, 2005,pp. 1-78.

Makgakga, Sello, and Percy Sepang. “Teaching and Learning the Mathematical Exponential and Logarithmic Functions: A Transformation Approach.” Mediterranean Journal of Social Sciences, vol. 4, no. 13, 2013, pp. 77-85.