## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises: 21

#### Answer

$x=-1$ or $x=3$

#### Work Step by Step

$2^{x^2-2x}=8$ Expressing the right side in terms of an exponent with base 2: $2^{x^2-2x}=2^3$ Taking base-2 log of both sides: $x^2-2x=3$ Thus, $x^2-2x-3=0$ Factorising the right side: $(x+1)(x-3)=0$ Therefore, $x=-1$ or $x=3$.

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