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1+6^(x+2) solve for x
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GPT-5 mini
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I need the right-hand side — an equation like 1 + 6^(x+2) = ? — to solve for x. Common possibilities:
- If you mean 1 + 6^(x+2) = c (constant), then for a real solution you must have c > 1. Solve:
6^(x+2) = c − 1
x + 2 = log_6(c − 1)
x = log_6(c − 1) − 2
- Example: if 1 + 6^(x+2) = 7, then 6^(x+2) = 6, so x + 2 = 1 and x = −1.
- If you meant 1 + 6^(x+2) = 0, there is no real solution (6^(x+2) > 0). In complex numbers:
6^(x+2) = −1 ⇒ e^{(x+2) ln 6} = −1 ⇒ (x+2) ln 6 = iπ(2k+1)
x = −2 + i·π(2k+1)/ln 6 for any integer k.
Tell me the right-hand side you intended and I’ll give the specific solution.
- If you mean 1 + 6^(x+2) = c (constant), then for a real solution you must have c > 1. Solve:
6^(x+2) = c − 1
x + 2 = log_6(c − 1)
x = log_6(c − 1) − 2
- Example: if 1 + 6^(x+2) = 7, then 6^(x+2) = 6, so x + 2 = 1 and x = −1.
- If you meant 1 + 6^(x+2) = 0, there is no real solution (6^(x+2) > 0). In complex numbers:
6^(x+2) = −1 ⇒ e^{(x+2) ln 6} = −1 ⇒ (x+2) ln 6 = iπ(2k+1)
x = −2 + i·π(2k+1)/ln 6 for any integer k.
Tell me the right-hand side you intended and I’ll give the specific solution.
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