Question

2^7x+3=64 уравнение......................

Answer 1

2^7x+3=2^6; 7x+3=6; 7x=6-3; 7x=3; x=3/7. Ответ: x=3/7.

Answer 2

To solve the equation 2^(7x) + 3 = 64, we need to find the value of 'x' that satisfies the equation. Let's go step by step:

Step 1: Subtract 3 from both sides of the equation to isolate the term with the exponent:

2^(7x) + 3 - 3 = 64 - 3

Step 2: Simplify the equation:

2^(7x) = 61

Step 3: Now, we need to express both sides of the equation in terms of the same base. Let's convert 61 to a power of 2:

Since 2^5 = 32 and 2^6 = 64, we can infer that 61 lies between 32 and 64. To get closer, we can try the average of 5 and 6 (the exponents for 32 and 64):

2^(5.5) ≈ 45.25

Step 4: We now know that 61 is greater than 32 and less than 45.25. Therefore, we can say:

2^5 < 61 < 2^(5.5)

Step 5: We can write 5.5 as a fraction (11/2):

2^5 < 61 < 2^(11/2)

Step 6: Now, rewrite the equation as a power with a common base of 2:

2^5 < 2^(7x) < 2^(11/2)

Step 7: Equate the exponents to solve for 'x':

7x = 11/2

Step 8: Solve for 'x':

x = (11/2) / 7 x = 11/14

So, the solution to the equation 2^(7x) + 3 = 64 is x = 11/14.