Question
Solve this indical equation:
(10)^(x) = 0.001
(10)^(x) = 0.001
Answers
Answer
(5)^(1-2x) = 1
Answer
Can you like do your work together with the base instead of separate calculations of the indices and base?
Answer
But what happened to the numbers 5 and 1, the bases?
Answered by
GPT-4o mini
To solve the exponential equation \( (10)^x = 0.001 \), we can first rewrite \( 0.001 \) in terms of a power of \( 10 \):
\[
0.001 = \frac{1}{1000} = \frac{1}{10^3} = 10^{-3}
\]
Now, we can rewrite the equation as:
\[
10^x = 10^{-3}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
x = -3
\]
Thus, the solution to the equation \( (10)^x = 0.001 \) is:
\[
\boxed{-3}
\]
\[
0.001 = \frac{1}{1000} = \frac{1}{10^3} = 10^{-3}
\]
Now, we can rewrite the equation as:
\[
10^x = 10^{-3}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
x = -3
\]
Thus, the solution to the equation \( (10)^x = 0.001 \) is:
\[
\boxed{-3}
\]
Answered by
GPT-4o mini
To solve the equation \( (5)^{1 - 2x} = 1 \), we start by recalling that any number raised to the power of 0 equals 1. Therefore, we can set the exponent equal to 0:
\[
1 - 2x = 0
\]
Now, solve for \( x \):
\[
1 = 2x
\]
\[
x = \frac{1}{2}
\]
Thus, the solution to the equation \( (5)^{1 - 2x} = 1 \) is:
\[
\boxed{\frac{1}{2}}
\]
\[
1 - 2x = 0
\]
Now, solve for \( x \):
\[
1 = 2x
\]
\[
x = \frac{1}{2}
\]
Thus, the solution to the equation \( (5)^{1 - 2x} = 1 \) is:
\[
\boxed{\frac{1}{2}}
\]
Answered by
GPT-4o mini
Sure! Let's solve the equation \( (5)^{1 - 2x} = 1 \) while keeping the base and the exponent together for clarity.
1. We start with the equation:
\[
(5)^{1 - 2x} = 1
\]
2. We know that for any base \( a \) (where \( a \neq 0 \)), \( a^0 = 1 \). Therefore, we can set the exponent equal to 0:
\[
1 - 2x = 0
\]
3. Solving for \( x \):
\[
1 - 2x = 0
\]
\[
1 = 2x
\]
\[
x = \frac{1}{2}
\]
Thus, the final solution is:
\[
\boxed{\frac{1}{2}}
\]
If you have any other specific approach in mind or need further clarification, feel free to ask!
1. We start with the equation:
\[
(5)^{1 - 2x} = 1
\]
2. We know that for any base \( a \) (where \( a \neq 0 \)), \( a^0 = 1 \). Therefore, we can set the exponent equal to 0:
\[
1 - 2x = 0
\]
3. Solving for \( x \):
\[
1 - 2x = 0
\]
\[
1 = 2x
\]
\[
x = \frac{1}{2}
\]
Thus, the final solution is:
\[
\boxed{\frac{1}{2}}
\]
If you have any other specific approach in mind or need further clarification, feel free to ask!
Answered by
GPT-4o mini
I understand your request now. Let's take into account the base and keep the calculations together. We'll analyze it with emphasis on the base \(5\) and the exponent.
Given the equation:
\[
(5)^{1 - 2x} = 1
\]
1. **Recognize the condition of the equation:** Since \( (5)^{1 - 2x} \) must equal 1, we can apply the property that states any non-zero base raised to the power of 0 equals 1. Therefore, we can conclude:
\[
1 - 2x = 0
\]
2. **Now solve for \(x\)** while keeping the equation balanced and highlighting the base and exponent:
- Start with the equation for the exponent:
\[
1 - 2x = 0
\]
- Rearranging this gives us:
\[
1 = 2x
\]
- Solving for \(x\):
\[
x = \frac{1}{2}
\]
Thus, highlighting the significance of the base \(5\) alongside the exponent process, we arrive at the solution:
\[
\boxed{\frac{1}{2}}
\]
If you were looking for something else in terms of formatting or explanation, please let me know!
Given the equation:
\[
(5)^{1 - 2x} = 1
\]
1. **Recognize the condition of the equation:** Since \( (5)^{1 - 2x} \) must equal 1, we can apply the property that states any non-zero base raised to the power of 0 equals 1. Therefore, we can conclude:
\[
1 - 2x = 0
\]
2. **Now solve for \(x\)** while keeping the equation balanced and highlighting the base and exponent:
- Start with the equation for the exponent:
\[
1 - 2x = 0
\]
- Rearranging this gives us:
\[
1 = 2x
\]
- Solving for \(x\):
\[
x = \frac{1}{2}
\]
Thus, highlighting the significance of the base \(5\) alongside the exponent process, we arrive at the solution:
\[
\boxed{\frac{1}{2}}
\]
If you were looking for something else in terms of formatting or explanation, please let me know!
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