((125)/(8))times((125)/(8))^(x)=((5)/(2))^(18)

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (125/8) * (125/8)^x = (5/2)^18

This article will guide you through the process of solving the equation (125/8) * (125/8)^x = (5/2)^18. We will break down the steps to make it easier to understand.

Step 1: Simplify the Equation

We can simplify the equation by expressing all the terms with the same base. Notice that:

• (125/8) can be written as (5/2)^3
• (5/2)^18 is already in its simplified form

Substituting these into our original equation, we get:

(5/2)^3 * (5/2)^(3x) = (5/2)^18

Step 2: Applying the Rule of Exponents

The rule of exponents states that when multiplying powers with the same base, we add the exponents. Applying this rule, we get:

(5/2)^(3+3x) = (5/2)^18

Step 3: Solving for x

Since the bases are the same, we can equate the exponents:

3 + 3x = 18

Now we solve for x:

• 3x = 15
• x = 5

Solution

Therefore, the solution to the equation (125/8) * (125/8)^x = (5/2)^18 is x = 5.