Find the solution for \( x \) in the equation \( 2(3)^{x}=8 \) \( x=-1.262 \) \( x=1.262 \) \( x=0.631 \) \( x=-0.631 \)

To solve the equation \( 2(3)^{x} = 8 \), we first divide both sides by 2, giving us \( (3)^{x} = 4 \). Then, we can express 4 as \( 2^2 \) and take logarithms of both sides or use the property of exponents. Let's write it in logarithmic form: \( x = \log_3(4) \). Now, using change of base formula yields \( x = \frac{\log(4)}{\log(3)} \approx 1.26186 \), which is approximately \( 1.262 \). So, the correct answer is \( x \approx 1.262 \). Did you know that logarithms were developed in the early 17th century by John Napier? They were initially created to simplify complex calculations, making it easier for scientists and astronomers of the time to perform multiplication and division through addition and subtraction! In real-world applications, logarithms are essential in fields like finance to model exponential growth, such as compound interest, and in biology to describe population growth rates. They're also used in the field of acoustics to measure sound intensity using the decibel scale, demonstrating just how versatile and practical these mathematical concepts can be!