Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 312: 67

$log_45\approx1.161$

Step 1. Multiply $u=4^{x}$ on both sides, we have $u^2-10-3u=0 \longrightarrow (u+2)(u-5)=0\longrightarrow u=-2,5$ Step 2. For $u=-2$, we have $4^x=-2 \longrightarrow $ no real solution. Step 3. For $u=5$, we have $4^x=5 \longrightarrow x=log_45\approx1.161$