Write the logarithmic equation y = ln (15x) in exponential form.

**Solution:-**

Recall y = log_{b} x is called the logarithmic form of the equation and x = b^{y} 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 = b^{y} , and y is the logarithm in y = log _{b} x and the exponent in x = b^{y}. Thus, a logarithm is an exponent.

The logarithmic function with base e is y = log _{e}x , defined by x = e^{y} for all positive numbers x and denoted by ln x = log _{e}x.

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.

e^{y} = 15x

Therefore, the exponential form of the equation y = ln (15x) is e^{y} = 15x.