Question

(1/8)^x-5=64 решить уравнение​

Answer 1

2^(-3x+15)=2^6

-3x+15=6

-3x=-9

x=3

Answer 2

To solve the equation (1/8)^x - 5 = 64, we need to isolate the variable x. Let's go step-by-step to find the solution:

Step 1: Add 5 to both sides of the equation to move the constant term to the right side:

(1/8)^x = 64 + 5

Step 2: Simplify the right side:

(1/8)^x = 69

Step 3: Now, rewrite 69 as a fraction with a base of 8:

69 = 8^2 + 8^1 + 8^0

Step 4: Substitute the right side of the equation with the rewritten fraction:

(1/8)^x = 8^2 + 8^1 + 8^0

Step 5: Now, write both sides of the equation with the same base:

8^(-3x) = 8^2 + 8^1 + 8^0

Step 6: Since the bases are the same, the exponents must be equal:

-3x = 2 + 1 + 0

Step 7: Simplify the right side:

-3x = 3

Step 8: Divide both sides by -3 to solve for x:

x = 3 / (-3)

Step 9: Simplify:

x = -1

So, the solution to the equation is x = -1.