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Advanced Math
/ Nonlinear functions
Difficulty: Medium
The exponential function is defined by , where is a positive constant. If , what is the value of ?
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Explanation
The correct answer is . It's given that the exponential function is defined by , where is a positive constant, and . It follows that when , . Substituting for and for in the given equation yields . Dividing each side of this equation by yields . Taking the cube root of both sides of this equation gives . Substituting for and for in the equation yields , or . Therefore, the value of is .