Question

2^(x)+5*2^(x-1)=7*2^(-5)

Answer 1

Ответ:

-4

Объяснение:

$2^x+5*2^{x-1}=7*2^{-5}\\\\2^{x-1}(2^{x-(x-1)}+5*1)=7*2^{-5}\\\\2^{x-1}(2^{x-x+1}+5)=7*2^{-5}\\\\2^{x-1}(2+5)=7*2^{-5}\\\\2^{x-1}*7=7*2^{-5}\\\\2^{x-1}=2^{-5}\\\\x-1=-5\\\\x=1-5\\\\x=-4$

Answer 2

To solve the equation 2^(x) + 5 * 2^(x-1) = 7 * 2^(-5), we can simplify the equation and solve for x. Let's go step by step:

First, let's simplify the equation using the properties of exponents:

2^(x) + 5 * 2^(x-1) = 7 * 2^(-5)

Rewriting 2^(x-1) as 2^(x) * 2^(-1):

2^(x) + 5 * 2^(x) * 2^(-1) = 7 * 2^(-5)

Combining the terms with the same base:

2^(x) + 5 * 2^(x) * (1/2) = 7 * 2^(-5)

Multiplying 5 * (1/2) gives us 5/2:

2^(x) + (5/2) * 2^(x) = 7 * 2^(-5)

Now, let's combine the terms with the same base:

(1 + 5/2) * 2^(x) = 7 * 2^(-5)

Simplifying 1 + 5/2 gives us 7/2:

(7/2) * 2^(x) = 7 * 2^(-5)

Now, let's cancel out the common factor of 7:

(1/2) * 2^(x) = 2^(-5)

To simplify the equation further, we can rewrite 2^(-5) as 1/2^(5):

(1/2) * 2^(x) = 1/2^(5)

Now, let's equate the exponents on both sides:

2^(x - 1) = 2^(-5)

Since the bases are the same, the exponents must be equal:

x - 1 = -5

Now, let's solve for x:

x = -5 + 1

x = -4

Therefore, the solution to the equation 2^(x) + 5 * 2^(x-1) = 7 * 2^(-5) is x = -4.