The graph of is shifted 3 units down and 2 units right. Which equation represents the new graph?
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The exponential form of 2187 is 3^7. This is because 3 raised to the power of 7 equals 2187. In exponential form, the base (3) is raised to the power of the exponent (7) to give the result (2187).
log2(8) = 3 means (2)3 = 8
The exponential form of 53 is 5^3. In exponential form, the base (5) is raised to the power of the exponent (3), which means 5 is multiplied by itself 3 times. So, 5^3 is equal to 5 x 5 x 5, which equals 125.
Since the logarithmic function is the inverse of the exponential function, then we can say that f(x) = 103x and g(x) = log 3x or f-1(x) = log 3x. As we say that the logarithmic function is the reflection of the graph of the exponential function about the line y = x, we can also say that the exponential function is the reflection of the graph of the logarithmic function about the line y = x. The equations y = log(3x) or y = log10(3x) and 10y = 3x are different ways of expressing the same thing. The first equation is in the logarithmic form and the second equivalent equation is in exponential form. Notice that a logarithm, y, is an exponent. So that the question becomes, "changing from logarithmic to exponential form": y = log(3x) means 10y = 3x, where x = (10y)/3.
Using the natural (base e) logs, written as "ln", 3 is eln(3) and 5 is eln(5). Or in base 10, 3=10log(3) and 5=10log(5). Check it out by taking log of both sides: log(3) = log(10log(3)) = log(3) x log(10) =log(3) x 1=log(3).