solve for a. \n$10^a = 1,000,000$\n$a = \\square$
solve for a. \n$10^a = 1,000,000$\n$a = \\square$
Answer
Explanation:
Step 1: Recall the definition of exponents
We know that (10^n) represents 1 followed by (n) zeros. For example, (10^1 = 10) (1 followed by 1 zero), (10^2=100) (1 followed by 2 zeros), etc.
Step 2: Analyze the number (1,000,000)
The number (1,000,000) is 1 followed by 6 zeros. So, using the definition of exponents with base 10, we can write (1,000,000 = 10^6).
Step 3: Solve for (a)
We have the equation (10^a=1,000,000), and we just found that (1,000,000 = 10^6). So, by the property of exponential functions (if (10^a = 10^b), then (a = b) when the base is the same and positive), we can conclude that (a = 6).
Answer:
(6)