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- - **exponential inequality**
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exponential inequalityConsider the inequality $9^x-a\cdot 3^x-a+3\leq 0,$ where $a$ is a real parameter. Find the value of $a$ so that $(1)$ The inequality has at least one negative solution $(2)$ The inequality has at least one positive solution |

write $u=3^x$ and solve the resulting quadratic. $3^x$ is monotonic increasing in $x$ so you can then solve for $x$ from $u$ and the inequalities remain unchanged. |

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