Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 31

$\{ 25.677\}$

Step 1. Rewrite the equation as $2(1.05)^x=7$ or $(1.05)^x=\frac{7}{2}$ Step 2. Take natural logarithm on both sides to get $x\ ln(1.05)=ln\frac{7}{2}$, thus $x=\frac{ln\frac{7}{2}}{ ln(1.05)}\approx25.677$ Step 3. Write answer in set form $\{ 25.677\}$