Write log aa = 15x in exponential form and find x to evaluate log aa for any a > 0, a ≠ 1.
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.
To write log aa = 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 aa = 15x is a15x = a.
Now, to find the value of x, set the exponents on both sides of the equation, a15x = 0, equal and solve.
15x = 1
Recall the log aa = 15x and x =. Substitute the value of x in the equation log aa = 15x and evaluate log aa, where a > 0 , a ≠ 1.
log aa = 15()
log aa = 1
Thus, the exponential form of the equation log aa = 15x is a15x = a and x = for any a > 0, a ≠ 1.