# Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4: 13

$x=4$

#### Work Step by Step

We are given the exponential equation $3^{1-x}=\frac{1}{27}$. We can express each side using a common base and then solve for $x$. $3^{1-x}=3^{-3}=\frac{1}{3^{3}}\frac{1}{27}$ Take the natural log of both sides. $ln(3^{1-x})=ln(3^{-3})$ $(1-x)ln(3)=-3ln(3)$ Divide both sides by $ln(3)$. $1-x=-3$ Subtract 1 from both sides. $-x=-4$ Divide both sides by -1. $x=4$

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