Question

Use the product rule of logarithms to write the completely expanded expression equivalent to ln(9x(2x 5))

Answer 1

Using the product rule of logarithms, the expression ln(9x(2x + 5)) can be expanded to ln(9) + ln(x) + ln(2x + 5).

Step-by-step explanation:

The product rule of logarithms states that the logarithm of a product of two numbers is the sum of the logarithms of those two numbers. We can apply this rule to the expression ln(9x(2x + 5)).

First, we can write the expression as the sum of two logarithms: ln(9x) + ln(2x + 5).

Then, we can expand ln(9x) by using the product rule, where 9x can be viewed as 9 times x, which becomes ln(9) + ln(x). Since there is no product to be broken down further in ln(2x + 5), it remains as is.

The final expanded expression using the product rule of logarithms is ln(9) + ln(x) + ln(2x + 5).

Answer 2

To expand the expression ln(9x(2x+5)), apply the product rule of logarithms. The expanded expression is ln(9x) + ln(2x+5).

Step-by-step explanation:

Using the product rule of logarithms which states that the logarithm of a product equals the sum of the logarithms of its factors. Applied to the natural logarithm function, it's expressed as ln(ab) = ln(a) + ln(b).

Subsequently, we can write expression ln(9x(2x 5)) as follows:

To expand the expression ln(9x(2x+5)), we can use the product rule of logarithms.

According to the product rule, the logarithm of a product of two numbers is equal to the sum of the logarithms of the individual numbers.

Therefore, ln(9x(2x+5)) can be expanded as ln(9x) + ln(2x+5).