Solve for \(X\) if \(4^{3 x -2}=26^{ x =1}\)
A. 6,694 B. 6,649 C. 6,469 D. 6,496 Correct Answer: AExplanation\(4^{3 x-2}=26^{x=1}\) Taking the logaritian of,woth sides \(\left(3 x+\frac{1}{2}\right) \log _{4}=(x+1) \log 26\) \(3 x \log 4-2 \log 4=x \log 26+\log 26 .\) \(3 x \log 4 t \log 26=\log 26+2 \log 4\) \(x(3 \log 4 \log 26)=\log 26+2 \log 4\) dividing both sides by \(3 \log 4-\log 26\) \begin{aligned} x &=\frac{\log 26+2 \log 4}{3 \log 4-\log 26} \\ =& \frac{1.4150+2(0.6021)}{3(0.6021)-1.4150} \\ =& \frac{2.6192} {0.3912}\\ =6.6914 \end{aligned}
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