What is 2 (log^3 8+log^3^Z) - log3 (3^4-7^2) written as a single logarithm

We are given the expression 2 (log^3 8+log^3^Z) - log3 (3^4-7^2) and is asked to simplify this expression. The rules that apply here is that with the same base, for logarithmics that are added, the simplified expression is the product of the two numbers. On the other hand, for subtraction operations, the simplified expression is the quotient of the two numbers. The coefficient before the logarithmic expression becomes the power of the numbers inside.

Thus,

2 (log^3 8+log^3^Z) - log3 (3^4-7^2) = 2 (log 3 (8*Z)) - log 3 (32))

= 2 log 3 (8Z/32) = 2 log 3 (Z/4)

Then, we move the coeffiicient of 2 inside which becomes,

= log 3 (Z/4) ^2 = log 3 (Z2/16)