Write log _{a}a = 15x in exponential form and find x to evaluate log _{a}a for any a > 0, a ≠ 1.

**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.

To write log _{a}a = 15x in exponential form, the variable a is treated as the base.

The expression 15x is the exponent.

Therefore, the exponential form of the equation log _{a}a = 15x is a^{15x} = a.

Now, to find the value of x, set the exponents on both sides of the equation, a^{15x} = 0, equal and solve.

15x = 1

x =

Recall the log _{a}a = 15x and x =. Substitute the value of x in the equation log _{a}a = 15x and evaluate log _{a}a, where a > 0 , a ≠ 1.

log _{a}a = 15()

log _{a}a = 1

Thus, the exponential form of the equation log _{a}a = 15x is a^{15x} = a and x = for any a > 0, a ≠ 1.