| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To solve the equation 3^(x - 3) + 10 = 19, we first isolate the exponential term by subtracting 10 from both sides: 3^(x - 3) = 19 - 10 3^(x - 3) = 9 Since 9 is 3^2, we can rewrite the equation as: 3^(x - 3) = 3^2 This means that x - 3 = 2, because the bases are the same. Solving for x, we add 3 to both sides: x = 2 + 3 x = 5 Therefore, the correct answer is: C. 5 |
C |
| deepseekr1 | To solve the equation \(3^{x – 3} + 10 = 19\), start by isolating the exponential term. Subtract 10 from both sides: \[ 3^{x – 3} = 19 - 10 \implies 3^{x – 3} = 9. \] Recognize that \(9 = 3^2\), so rewrite the equation as: \[ 3^{x – 3} = 3^2. \] Since the bases are equal, the exponents must also be equal: \[ x – 3 = 2. \] Solving for \(x\) gives: \[ x = 2 + 3 = 5. \] Verify by substituting \(x = 5\) back into the original equation: \(3^{5-3} + 10 = 3^2 + 10 = 9 + 10 = 19\), which is correct. Answer: **C** |
C |
| gpto1 | C | C |
| GPT-4o | To solve the equation \(3^{(x - 3)} + 10 = 19\), we first isolate the exponential term: \[3^{(x - 3)} + 10 = 19\] Subtract 10 from both sides: \[3^{(x - 3)} = 9\] We know that 9 can be written as a power of 3: \[9 = 3^2\] Thus, we have: \[3^{(x - 3)} = 3^2\] Since the bases are the same, we can set the exponents equal to each other: \[x - 3 = 2\] Solving for \(x\): \[x = 2 + 3\] \[x = 5\] So, the answer is: C. 5 |
C |
| llama3.1-70B-Instruct | B |
C |
| llama3.1-405B-Instruct | To solve the equation 3^(x - 3) + 10 = 19, we first isolate the exponential term by subtracting 10 from both sides: 3^(x - 3) = 19 - 10 3^(x - 3) = 9 Now, we notice that 9 is a power of 3, specifically 3^2. Therefore, we can equate the exponents: x - 3 = 2 To solve for x, we add 3 to both sides: x = 2 + 3 x = 5 So, the correct answer is: C. 5 |
C |
| DeepSeek-Coder-V2 | B. 4 | C |
| Qwen2-72B-Instruct | B. 4 | C |
| baichuan4 | C | C |
| doubao | First, subtract 10 from both sides of the equation: 3^(x – 3) = 19 - 10 = 9. Then 3^(x – 3) = 3^2, so x - 3 = 2, and x = 2 + 3 = 5. So the answer is C. |
C |
| minimax | To solve for x, we first isolate the term with the exponent: 3^(x – 3) + 10 = 19 Subtract 10 from both sides: 3^(x – 3) = 9 Now we recognize that 9 is a power of 3, specifically 3^2: 3^(x – 3) = 3^2 Since the bases are the same, we can set the exponents equal to each other: x – 3 = 2 Now solve for x: x = 2 + 3 x = 5 The correct answer is: C. 5 |
C |
| kimi | To solve for x, we start with the given equation: \[ 3^{x - 3} + 10 = 19 \] First, we subtract 10 from both sides to isolate the exponential term: \[ 3^{x - 3} = 19 - 10 \] \[ 3^{x - 3} = 9 \] Next, we recognize that 9 is a power of 3: \[ 3^2 = 9 \] So, we can set the exponents equal to each other: \[ x - 3 = 2 \] Finally, we solve for x by adding 3 to both sides: \[ x = 2 + 3 \] \[ x = 5 \] The correct answer is C. 5. |
C |
| wenxinyiyan | C Explanation: Given the equation $3^{x - 3} + 10 = 19$, we can subtract 10 from both sides to get: $3^{x - 3} = 9$ Since $3^2 = 9$, we can write: $3^{x - 3} = 3^2$ Comparing the exponents, we get: $x - 3 = 2$ Solving for x, we have: $x = 5$ |
C |
| zhipu | To solve the equation \( 3^{(x - 3)} + 10 = 19 \), we need to isolate \( x \). Here are the steps: 1. Subtract 10 from both sides of the equation: \[ 3^{(x - 3)} + 10 - 10 = 19 - 10 \] Simplifying this, we get: \[ 3^{(x - 3)} = 9 \] 2. Recognize that \( 9 \) can be written as \( 3^2 \): \[ 3^{(x - 3)} = 3^2 \] 3. Since the bases are the same, we can equate the exponents: \[ x - 3 = 2 \] 4. Solve for \( x \) by adding 3 to both sides: \[ x - 3 + 3 = 2 + 3 \] Simplifying this, we get: \[ x = 5 \] Therefore, the correct answer is \( \boxed{C} \). |
C |
| gpto1 | C | C |
| deepseekv3 | To solve the equation \( 3^{x - 3} + 10 = 19 \), follow these steps: 1. Subtract 10 from both sides: \[ 3^{x - 3} = 19 - 10 \] \[ 3^{x - 3} = 9 \] 2. Recognize that \( 9 \) can be written as \( 3^2 \): \[ 3^{x - 3} = 3^2 \] 3. Since the bases are the same, set the exponents equal to each other: \[ x - 3 = 2 \] 4. Solve for \( x \): \[ x = 2 + 3 \] \[ x = 5 \] Therefore, the correct answer is \( C. 5 \). |
C |