42.What is the value of xin 5cdot ((1)/(4))^3x+4=40

To solve the equation \(5 \cdot \left(\frac{1}{4}\right)^{3x+4} = 40\), we can follow these steps:1. Divide both sides of the equation by 5:\(\left(\frac{1}{4}\right)^{3x+4} = 8\)2. Take the logarithm of both sides of the equation:\(\log\left(\left(\frac{1}{4}\right)^{3x+4}\right) = \log(8)\)3. Use the power rule of logarithms to simplify the left side:\((3x+4) \cdot \log\left(\frac{1}{4}\right) = \log(8)\)4. Divide both sides of the equation by \(\log\left(\frac{1}{4}\right)\):\(3x+4 = \frac{\log(8)}{\log\left(\frac{1}{4}\right)}\)5. Subtract 4 from both sides of the equation:\(3x = \frac{\log(8)}{\log\left(\frac{1}{4}\right)} - 4\)6. Divide both sides of the equation by 3:\(x = \frac{1}{3} \cdot \left(\frac{\log(8)}{\log\left(\frac{1}{4}\right)} - 4\right)\)Now, we can simplify the expression further:\(\log\left(\frac{1}{4}\right) = \log(4^{-1}) = -\log(4)\)\(\log(8) = \log(2^3) = 3\log(2)\)So, the expression becomes:\(x = \frac{1}{3} \cdot \left(\frac{3\log(2)}{-\log(4)} - 4\right)\)We can simplify the fraction inside the parentheses:\(\frac{3\log(2)}{-\log(4)} = \frac{3\log(2)}{-2\log(2)} = -\frac{3}{2}\)So, the expression becomes:\(x = \frac{1}{3} \cdot \left(-\frac{3}{2} - 4\right)\)Simplifying the expression inside the parentheses: So, the final expression for is:\(x = \frac{1}{3} \cdot \left(-\frac{11}{2}\right) = -\frac{11}{6}\)Therefore, the value of in the equation \(5 \cdot \left(\frac{1}{4}\right)^{3x+4} = 40\) is .