Precalculus Textbook 8th Edition Section 3.1 Exercise 40 Solution
Question:
Use the properties of exponents to prove that two of the given following three exponential functions are identical.
(a) \[ y_{1}=4^{3x-2} \]
(b) \[ y_{2}=2(2^{3x-2}) \]
(c) \[ y_{3}=2^{3x-1} \]
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Solution:
(a) Given that \[ y_{1}=4^{3x-2}\Rightarrow y_{1}=\frac{4^{3x}}{4^{2}}\Rightarrow y_{1}=\frac{2^{6x}}{16}\].
(b) Given that \[ y_{2}=2(2^{3x-2})\Rightarrow y_{2}=2\times \frac{2^{3x}}{2^{2}}\Rightarrow y_{2}=\frac{2^{3x}}{2}\].
(c) Given that \[ y_{3}=(2^{3x-1})\Rightarrow y_{3}=2\times \frac{2^{3x}}{2^{1}}\Rightarrow y_{2}=\frac{2^{3x}}{2}\].
Hence, we get that the functions given in the options (b) and (c) are identical.
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