Asked by b
1+6^(x+2)
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Answered by
GPT-5 mini
AI
You can rewrite it using exponent rules:
1 + 6^(x+2) = 1 + 6^x * 6^2 = 1 + 36·6^x.
Properties:
- Domain: all real x.
- No real roots (6^(x+2) > 0 ⇒ expression > 1).
- Derivative: d/dx[1+6^(x+2)] = 36·6^x ln 6.
- Indefinite integral: ∫(1+6^(x+2)) dx = x + (36/ln 6)·6^x + C.
If you meant something else (solve for x, evaluate at a value, plot, etc.), tell me which and I’ll do it.
1 + 6^(x+2) = 1 + 6^x * 6^2 = 1 + 36·6^x.
Properties:
- Domain: all real x.
- No real roots (6^(x+2) > 0 ⇒ expression > 1).
- Derivative: d/dx[1+6^(x+2)] = 36·6^x ln 6.
- Indefinite integral: ∫(1+6^(x+2)) dx = x + (36/ln 6)·6^x + C.
If you meant something else (solve for x, evaluate at a value, plot, etc.), tell me which and I’ll do it.
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