Question

5^(3x)-2*5^(3x-1)-3*5^(3x-2)=60

Answer 1

5^3x=t

t-2t/5-3t/25=60 умножаем на 25

25t-10t-3t=1500

12t=1500

t=125

5^3x=5^3

3x=3

x=1

 

Answer 2

To solve the equation 5^(3x) - 2 * 5^(3x-1) - 3 * 5^(3x-2) = 60, we can follow these steps:

Step 1: Simplify the equation Let's simplify the equation by combining like terms and using the properties of exponents.

5^(3x) - 2 * 5^(3x-1) - 3 * 5^(3x-2) = 60 (5^3)^x - 2 * (5^3)^(x-1) - 3 * (5^3)^(x-2) = 60 125^x - 2 * 125^(x-1) - 3 * 125^(x-2) = 60 125^x - 2 * 125 * 125^(x-1) - 3 * 125^2 * 125^(x-2) = 60 125^x - 250 * 125^(x-1) - 375 * 125^(x-2) = 60

Step 2: Simplify further Now let's simplify the equation further by dividing everything by 125^(x-2) to eliminate the common base.

(125^x) / (125^(x-2)) - (250 * 125^(x-1)) / (125^(x-2)) - (375 * 125^(x-2)) / (125^(x-2)) = 60 125^(x - (x - 2)) - 250 * 125^(x - (x - 1)) - 375 * 125^(x - (x - 2)) = 60 125^2 - 250 * 125 - 375 = 60 15625 - 31250 - 375 = 60 -15625 = 60

Step 3: Conclusion After simplifying the equation, we obtained -15625 = 60. However, this is not a true statement. Therefore, there is no solution to the given equation.

Hence, the equation 5^(3x) - 2 * 5^(3x-1) - 3 * 5^(3x-2) = 60 has no solution.