Question

6^x+6^(x+1)=2^x+2^(x+1)+2^(x+2)

Answer 1

6^х+6^(х+1)=2^х+2^(х+1)+2^(х+2)
(1+6)6^х=(1+2+2^2)2^х
7*6^х=(1+2+4)2^х
6^х=2^х
3^х=3
х=0

Answer 2

To solve the equation 6^x + 6^(x+1) = 2^x + 2^(x+1) + 2^(x+2), we can simplify the equation and solve for x.

Let's break it down step by step:

1. Distribute the exponents: 6^x + 6 * 6^x = 2^x + 2 * 2^x + 4 * 2^x

2. Combine like terms: 6^x + 6 * 6^x = 2^x + 2^x + 2^x + 4 * 2^x

3. Simplify the left side of the equation: 1 * 6^x + 6 * 6^x = 1 * 2^x + 1 * 2^x + 1 * 2^x + 4 * 2^x

   7 * 6^x = 7 * 2^x

4. Divide both sides by 7: (7 * 6^x) / 7 = (7 * 2^x) / 7

   6^x = 2^x

5. Take the logarithm of both sides (with any base): log(6^x) = log(2^x)

   x * log(6) = x * log(2)

6. Cancel out the x terms: log(6) = log(2)

Since log(6) is not equal to log(2), we don't have a valid solution for x. Therefore, the original equation has no solution.