Final answer:
To find the value of log4(t⁸x¹²)/(y⁴), use the properties of logarithms and substitute the given values to simplify the expression.
Step-by-step explanation:
The question involves using the properties of logarithms, particularly the power rule (logb(mn) = n · logb(m)), the product rule (logb(mn) = logb(m) + logb(n)), and the quotient rule (logb(m/n) = logb(m) - logb(n)) to simplify the given expression log4 (t⁸x¹²)/(y⁴).
To find the value of log4(t⁸x¹²)/(y⁴), we can use the properties of logarithms. Start by applying the power rule of logarithms: log4(t⁸x¹²)/(y⁴) = (8log4t + 12log4x - 4log4y).
Now substitute the given values: (8(7.6) + 12(-7.66) - 4(8.39)).
Simplify the expression: (60.8 - 91.92 - 33.56).
Therefore, log4(t⁸x¹²)/(y⁴) ≈ -64.68.