Write the following expression as a sum or difference of logarithms with no exponents. Assume all variables represent positive values Simplify your answer completely. log_(4)((y^16z^4)/(sqrt [2](w+15))) log_(4)((y^16z^4)/(sqrt [3](w+15)))=square Importance of Concept Like many operations in mathematics, the process of expanding a logarithm might seem abstract and not useful; however, many challenging problems in calculus (specifically, differential calculus can be greatly simplified by applying logarithms and expanding the resulting expression.

To write the given expression as a sum or difference of logarithms with no exponents, we can use the properties of logarithms. The given expression is: We can use the quotient rule of logarithms, which states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. So, we can rewrite the expression as: Next, we can use the product rule of logarithms, which states that the logarithm of a product is equal to the sum of the logarithms of the factors. Applying the product rule to the first term, we get: Now, we can simplify the expression further by using the power rule of logarithms, which states that the logarithm of a number raised to an exponent is equal to the exponent times the logarithm of the number. Applying the power rule to the terms, we get: Therefore, the expanded form of the given expression is: This expression is now written as a sum and difference of logarithms with no exponents.