What is exponential and logarithmic graphs?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. Below are pictured graphs of the form y = logax when a > 1 and when 0 < a < 1.
How do you tell if a graph is exponential or logarithmic?
This reflects the graph about the line y=x. As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve….Comparison of Exponential and Logarithmic Functions.
| Exponential | Logarithmic | |
|---|---|---|
| Function | y=ax, a>0, a≠1 | y=loga x, a>0, a≠1 |
| Domain | all reals | x > 0 |
| Range | y > 0 | all reals |
What is exponential and logarithmic equations?
An exponential equation is an equation in which the variable appears in an exponent. A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.
How did exponential equation is expressed in logarithmic form?
To convert from exponential to logarithmic form, we follow the same steps in reverse. We identify the base b, exponent x, and output y. Then we write x=logb(y) x = l o g b ( y ) .
What are the key features of logarithmic and exponential graphs?
The logarithmic function graph passes through the point (1, 0), which is the inverse of (0, 1) for an exponential function. The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right if 0 < b < 1.
How do you find the logarithmic equation?
The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logb x is read, “y equals log to the base b of x,” or more simply, “y equals log base b of x.” As with exponential functions, b > 0 and b ≠ 1….
| x = 3y | y |
|---|---|
| −1 | |
| 1 | 0 |
| 3 | 1 |
| 9 | 2 |
How can logarithms be used to solve exponential equations?
How To: Given an exponential equation in which a common base cannot be found, solve for the unknown. Apply the logarithm of both sides of the equation. If one of the terms in the equation has base 10, use the common logarithm. If none of the terms in the equation has base 10, use the natural logarithm.
