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to solve an equation like 3^(2x+1) = 27, you must first give both sides a common base before using the one-to-one property. true or false
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False.
You don't have to rewrite both sides with the same base — you can also take logarithms. Example:
Method 1 (common base): 27 = 3^3, so 3^(2x+1) = 3^3 ⇒ 2x+1 = 3 ⇒ x = 1.
Method 2 (logs): take natural log: (2x+1) ln 3 = ln 27 ⇒ 2x+1 = ln 27 / ln 3 = 3 ⇒ x = 1.
(If you do use the one-to-one property directly, the bases must match and be positive ≠ 1.)
You don't have to rewrite both sides with the same base — you can also take logarithms. Example:
Method 1 (common base): 27 = 3^3, so 3^(2x+1) = 3^3 ⇒ 2x+1 = 3 ⇒ x = 1.
Method 2 (logs): take natural log: (2x+1) ln 3 = ln 27 ⇒ 2x+1 = ln 27 / ln 3 = 3 ⇒ x = 1.
(If you do use the one-to-one property directly, the bases must match and be positive ≠ 1.)
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