Problem 731

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

 

Solution:-

 

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

x = \frac{1}{15}

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

log aa = 15(\frac{1}{15})

log aa = 1

Thus, the exponential form of the equation log aa = 15x is a15x = a and x = \frac{1}{15} for any a > 0, a ≠ 1.

 

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