Exponential form is ax = b.
Logarithmic form is logab = x.
For example, 102 = 100 is the same as log10100 = 2.
Another example: 53 = 125 is the same as log5125 = 3.
If there is no number under the log (for example, log3), the the number is understood to be ten. For example, log8 is the same as log108.
A natural log uses the symbol ln. In this case, the number is understood to be e (which equals about 2.718). For example, ln5 is the same as loge5 (which the same as log2.7185).
Exponential growth
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Logarithmic equation
Logarithmic functions are converted to become exponential functions because both are inverses of one another.
The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then y = LN(x), is the same as sayinig x = ey.
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.
Logb (x)=y is called the logarithmic form where logb means log with base b So to put this in exponential form we let b be the base and y the exponent by=x Here is an example log2 8=3 since 23 =8. In this case the term on the left is the logarithmic form while the one of the right is the exponential form.
Exponential and logarithmic functions are inverses of each other.
The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)
Exponential growth
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
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.
No. The inverse of an exponential function is a logarithmic function.
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Here's logarithmic form: 1 log ^ 10 Now here's the same thing in exponential form: 10^1 So basically it's just two different ways of writing the same thing. Remember that log is always base "10" unless otherwise specified
Exponential and logarithmic functions are different in so far as each is interchangeable with the other depending on how the numbers in a problem are expressed. It is simple to translate exponential equations into logarithmic functions with the aid of certain principles.