In Exercises 125–128, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.logb (xy)^5 = (logb x + logb y)^5

Logarithms have specific properties that govern their behavior, including the product, quotient, and power rules. The product rule states that logb(xy) = logb(x) + logb(y), while the power rule states that logb(x^n) = n * logb(x). Understanding these properties is essential for manipulating logarithmic expressions correctly.

When dealing with logarithmic functions, exponentiation plays a crucial role. The expression (logb x)^n does not equal logb(x^n). Instead, the power must be applied to the argument of the logarithm, not the logarithm itself. This distinction is vital for accurately interpreting and transforming logarithmic equations.

In algebra, determining the truth value of statements often involves verifying their correctness through established rules and properties. A statement is true if it holds under all conditions defined by the mathematical properties, while a false statement can be corrected by applying the appropriate mathematical rules. This process is fundamental in exercises that require validation of algebraic expressions.