(2%2F3)%5Ex%3D(1%2F4)(16%2F27).jpeg "(1/2)(2/3)^x=(1/4)(16/27)")
Solving the Equation: (1/2)(2/3)^x = (1/4)(16/27)
This article will guide you through the steps of solving the equation (1/2)(2/3)^x = (1/4)(16/27).
Simplifying the Equation
First, we simplify both sides of the equation:
- Left side: (1/2)(2/3)^x can be rewritten as (2/3)^x / 2
- Right side: (1/4)(16/27) simplifies to 4/27, which can be expressed as (2/3)^3 / 2
Now our equation looks like this: (2/3)^x / 2 = (2/3)^3 / 2
Isolate the Exponential Term
To isolate the term with the exponent, we multiply both sides of the equation by 2:
(2/3)^x = (2/3)^3
Solving for x
Since both sides of the equation now have the same base, we can equate the exponents:
x = 3
Solution
Therefore, the solution to the equation (1/2)(2/3)^x = (1/4)(16/27) is x = 3.