Questions: Write the equation in exponential form. log(1/1,000,000) = -6 The equation in exponential form is □.

Solution Steps

To convert a logarithmic equation to its exponential form, we use the property that if $\log_b(a) = c$, then the equivalent exponential form is $b^c = a$. In this case, the base of the logarithm is 10 (common logarithm), and we need to express the given logarithmic equation in exponential form.

We start with the logarithmic equation given by

$$\log \left(\frac{1}{1,000,000}\right) = -6.$$

To convert this to exponential form, we recognize that the base of the logarithm is 10. Thus, we can express the equation as:

$$10^{-6} = \frac{1}{1,000,000}.$$

Next, we simplify the right side of the equation. The fraction $\frac{1}{1,000,000}$ can be expressed in scientific notation as:

$$\frac{1}{1,000,000} = 1 \times 10^{-6}.$$

Now we can confirm that the exponential form of the logarithmic equation is indeed:

$$10^{-6} = 1 \times 10^{-6}.$$

This shows that the conversion is correct.

Final Answer