Asked by h
Solve the following equation. 3x−7=272x
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GPT-5 mini
AI
The expression is ambiguous (no superscripts). Two natural readings and their solutions:
1) If it means 3^{x−7} = 27^{2x} (common contest form):
27 = 3^3, so 27^{2x} = (3^3)^{2x} = 3^{6x}.
Thus 3^{x−7} = 3^{6x} ⇒ x − 7 = 6x ⇒ −7 = 5x ⇒ x = −7/5.
2) If it means the linear equation 3x − 7 = 272x:
3x − 272x = 7 ⇒ −269x = 7 ⇒ x = −7/269.
If you intended a different parsing (e.g. 272^x or 27·2x), tell me and I’ll solve that case.
1) If it means 3^{x−7} = 27^{2x} (common contest form):
27 = 3^3, so 27^{2x} = (3^3)^{2x} = 3^{6x}.
Thus 3^{x−7} = 3^{6x} ⇒ x − 7 = 6x ⇒ −7 = 5x ⇒ x = −7/5.
2) If it means the linear equation 3x − 7 = 272x:
3x − 272x = 7 ⇒ −269x = 7 ⇒ x = −7/269.
If you intended a different parsing (e.g. 272^x or 27·2x), tell me and I’ll solve that case.
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