Write the logarithmic equation y = ln (15x) in exponential form.
Recall y = logb x is called the logarithmic form of the equation and x = by is called the exponential form of the equation. The number b is called the base in both in both y = log b x and x = by , and y is the logarithm in y = log b x and the exponent in x = by. Thus, a logarithm is an exponent.
The logarithmic function with base e is y = log ex , defined by x = ey for all positive numbers x and denoted by ln x = log ex.
Therefore, the logarithmic function y = ln (15x) can be written as y = log e(15x). To write y = ln (15x) in exponential form, the number e is treated as the case and y will be placed as exponent.
Now write y = ln (15x) in the exponential form.
ey = 15x
Therefore, the exponential form of the equation y = ln (15x) is ey = 15x.