Final answer:
The logarithmic expression log5(√ab) can be expanded using the power rule to 1/2 * log5(ab) and then further using the product rule to 1/2 * (log5a + log5b), resulting in its expanded form.
Step-by-step explanation:
The logarithmic expression log5(√ab) can be expanded using properties of logarithms. First, recall that the square root of a number is the same as raising that number to the one-half power. The expression √ab is equivalent to (ab)1/2.
Using the power rule of logarithms, which states that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, the expression can be rewritten as 1/2 * log5(ab).
Next, apply the product rule of logarithms, which says that the logarithm of a product is equal to the sum of the logarithms of the factors to further expand the equation. This gives us 1/2 * (log5a + log5b).
Combining these concepts we get the final expanded form of the given logarithmic expression.