Let’s solve each of these equations by converting them to logarithmic form.

1. (a) $10^x = 1,000,000$

   To solve for $x$, rewrite the equation in logarithmic form: $x = \log_{10}(1,000,000)$ Since $1,000,000 = 10^6$, we find: $x = 6$

2. (b) $10^x = 0.0001$

   Rewrite this in logarithmic form: $x = \log_{10}(0.0001)$ Since $0.0001 = 10^{-4}$, we have: $x = -4$

3. (c) $10^x = \frac{1}{1000}$

   Rewrite in logarithmic form: $x = \log_{10}\left(\frac{1}{1000}\right)$ Since $\frac{1}{1000} = 10^{-3}$, we find: $x = -3$

So, the answers are:

• (a) $x = 6$
• (b) $x = -4$
• (c) $x = -3$

Would you like further explanations on logarithmic conversions or have any questions?

Here are five related questions to deepen your understanding:

1. How would you solve $2^x = 128$ using logarithmic form?
2. What is the process to solve exponential equations without a calculator?
3. Can you explain why $\log_{10}(0.0001) = -4$?
4. How would you approach a problem like $5^x = 1/25$ using logarithms?
5. What is the difference between natural logarithms and common logarithms?

Tip: When solving exponential equations, converting them to logarithmic form simplifies the process, especially when powers of 10 are involved.