Actually, the base of \(\displaystyle 3^{2x}\) is 3! Of course that is the equal to \(\displaystyle (3^2)^x= 9^x\) which base 9. \(\displaystyle f(x)= 8^{\frac{4}{3}ax}\) has base 8. Using the "laws of exponents", \(\displaystyle 8^{4/3}= (8^{1/3})^4\) and, since \(\displaystyle 2^3= 8\), \(\displaystyle 8^{1/3}= 2\) so \(\displaystyle 8^{4/3}= 2^4= 16\) so that \(\displaystyle 8^{\frac{4}{3}x}= 16^x\).RidiculousName said:I was wondering if anyone could point me to a set of rules for finding the base of an exponential function? I can figure out that the base of \(\displaystyle f(x)=7^x\) is 7 and the base of \(\displaystyle f(x)=3^{2x}\) is 9 but even though I know \(\displaystyle f(x)=8^{\frac{4}{3}x}\) has a base of 16, I don't know how that answer was reached.
An exponential function is a mathematical function in the form of f(x) = ab^x, where a and b are constants and x is the independent variable. The base, b, is a positive number greater than 1, and as the value of x increases, the value of f(x) grows at an increasing rate.
To find the base of an exponential function, you can use the following steps:
Yes, as long as the points are not on the horizontal axis (x-axis). This is because the logarithm of 0 is undefined, so you cannot use points with a y-value of 0.
Yes, you can also use logarithms to find the base of an exponential function. The steps for this method are as follows:
Finding the base of an exponential function is important because it helps us understand the behavior and growth rate of the function. The base determines how quickly the function grows or decays, and it can also affect the shape of the graph. By finding the base, we can make predictions and draw conclusions about the function.