Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 34

$\{ 1917.096\}$

Step 1. Rewrite the equation as $(1.024)^{x-1900}=\frac{3}{2}$ Step 2. Take natural logarithm on both sides to get $(x-1900)\ ln(1.024)=ln\frac{3}{2}$, thus $x=1900+\frac{ln\frac{3}{2}}{ ln(1.024)}\approx1917.096$ Step 3. Write answer in set form $\{ 1917.096\}$