Question

2^(x-4)+2^(x-3)+2^(x)=5^(x+1)-5^(x)

Answer 1

Решение задания прилагаю

Answer 2

Ответ:

$2^{x-4} +2^{x-3} +2^{x} =5^{x+1} -5^{x} \\\\\frac{19}{16} =2^{-x} *5^{x+1} -(\frac{5}{2} )^{x} \\\\e^{log5(x+1)-log2x}-(\frac{5}{2})=\frac{19}{16} \\\\-4y=\frac{19}{16} \\\\y=-\frac{19}{64} \\\\-(\frac{5}{2} )^{x} =-\frac{19}{64} \\\\(\frac{5}{2} )^{x} =\frac{19}{64} \\\\x=-\frac{log\frac{64}{19} }{log\frac{5}{2} }$

Answer 3

The given equation is:

$2^{x-4} + 2^{x-3} + 2^x = 5^{x+1} - 5^x.$

To solve for $x$, we can start by simplifying both sides of the equation. Let's break down each side step by step.

1. Simplify the left side: $2^{x-4} + 2^{x-3} + 2^x$

   Since all terms have a common base of 2, we can combine them using the properties of exponents: $2^{x-4} + 2^{x-3} + 2^x = 2^{x-4} + 2^{x-4} + 2^{x-4} + 2^x = 3 \cdot 2^{x-4} + 2^x.$

2. Simplify the right side: $5^{x+1} - 5^x$

   Here, we also have terms with a common base of 5, so we can combine them: $5^{x+1} - 5^x = 5^x \cdot 5 - 5^x = 5 \cdot 5^x - 5^x = 4 \cdot 5^x.$

So, the equation becomes: $3 \cdot 2^{x-4} + 2^x = 4 \cdot 5^x.$

Now, we have a single equation in terms of $x$, and we need to solve for $x$. Unfortunately, this equation doesn't have a simple analytical solution that can be expressed in terms of elementary functions. You might need to use numerical methods or approximation techniques to find an approximate solution.

If you're looking for an exact solution, you might need to use specialized mathematical software or tools to find a numerical approximation for $x$.