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(1/2)(2/3)^x=(1/4)(16/27)

2 min read Jun 16, 2024
(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.

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