Okay, let's see. The problem is to solve for x in the equation 10^x minus 10 equals 9990. So, the equation is 10^x - 10 = 9990. Hmm, I need to find the value of x that satisfies this equation.

First, I should isolate the term with x. That means I need to get rid of the -10 on the left side. To do that, I can add 10 to both sides of the equation. Let me write that down:

10^x - 10 + 10 = 9990 + 10

Simplifying both sides, the -10 and +10 on the left cancel out, so we have:

10^x = 10000

Okay, so now the equation simplifies to 10 raised to the power of x equals 10,000. Now, I need to solve for x here. Since the base is 10, maybe taking the logarithm base 10 would help. Remember, logarithms are the inverse operations of exponentials. So, if I take log base 10 of both sides, that should do the trick.

Let me write that step:

log₁₀(10^x) = log₁₀(10000)

Using the logarithm power rule, log_b(a^c) = c * log_b(a), so the left side simplifies to x * log₁₀(10). But log base 10 of 10 is 1, right? Because 10^1 = 10. So that simplifies the left side to just x. Therefore:

x = log₁₀(10000)

Now, what is log base 10 of 10,000? Well, 10,000 is 10^4 because 10 multiplied by itself four times is 10,000. So, 10^4 = 10,000. Therefore, log₁₀(10,000) is 4. Hence, x equals 4.

Wait, but let me verify that again. If I substitute x = 4 back into the original equation, does it hold true?

Original equation: 10^x - 10 = 9990

Substituting x = 4:

10^4 - 10 = 10000 - 10 = 9990

Yes, that's exactly the right-hand side of the equation. So, 9990 equals 9990. That checks out. So, x = 4 is indeed the correct solution.

Alternatively, maybe there's another way to approach this without using logarithms. Let me think. Since 10^x = 10000, and 10000 is 10^4, then x must be 4. So, that's another way to see it. Since 10^4 is 10,000, which is the same as 10^x, so x must be 4. That's straightforward.

Therefore, the answer is 4. Let me just recap the steps to make sure I didn't skip anything. The original equation is 10^x - 10 = 9990. Adding 10 to both sides gives 10^x = 10000. Recognizing that 10000 is 10^4, so x is 4. Substituting back confirms the solution. Seems solid.

I don't think there are any other possible solutions here because exponential functions like 10^x are one-to-one, meaning each input x corresponds to exactly one output, and vice versa. Therefore, there's only one solution. So, x must be 4. Yeah, that makes sense. I can't think of any mistakes here. The steps are straightforward and verify correctly. So, the answer should be 4.
Therefore, the final answer is $\boxed{4}$.
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