What is the potential solution to the equation log4(2) x log4(5) x 18?

Finding the Solution

To solve the equation log4(2) x log4(5) x 18, we first need to clarify and simplify the expression, as it appears to be an equation rather than a singular expression.

The expression is made up of logarithmic components. Let’s break it down:

Step 1: Understanding Logarithms

The logarithm, log4(b), refers to the power to which the base (4) must be raised to produce the number b. For example, log4(2) asks the question, “4 raised to what power gives 2?”

Step 2: Simplifying the Equation

Based on the given expression, we can identify:

Calculate log4(2): Using change of base formula, we can calculate this as 1/2 because 4^(1/2) = 2.
Calculate log4(5): This value is less straightforward, and numerical approximations can give us log4(5) ≈ 1.161.

Now, we multiply the results:

Step 3: Numerical Calculation

Let’s denote the values:

A = log4(2) ≈ 0.5
B = log4(5) ≈ 1.161

Thus, the product becomes:

A * B * 18 ≈ 0.5 * 1.161 * 18

Step 4: Final Calculation

Carrying out the multiplication:

0.5 * 1.161 = 0.5805

0.5805 * 18 ≈ 10.437

Conclusion

The potential solution culminates to be approximately 10.437.