Question

Simplify ln(49) - ln(2) + ln(4) = ln(a) where a is a positive integer.

A. ln(100)
B. ln(7)
C. ln(98)
D. ln(12)

Answer 1

Using logarithm properties, ln(49) - ln(2) + ln(4) simplifies to ln(98), which means that a = 98 as per the equation ln(a).

Step-by-step explanation:

When simplifying ln(49) - ln(2) + ln(4), we can use the properties of logarithms to combine the terms. The difference of two logarithms, such as ln(49) - ln(2), can be expressed as the logarithm of the quotient of the two numbers, thanks to the property ln(a) - ln(b) = ln(a/b). Combining the terms, we get:

• ln(49) - ln(2) = ln(49/2)
• ln(49) - ln(2) + ln(4) = ln(49/2) + ln(4)
• ln(49/2) + ln(4) = ln((49/2) × 4)
• ln((49/2) × 4) = ln(49 × 2)
• ln(49 × 2) = ln(98)

Therefore, ln(49) - ln(2) + ln(4) = ln(98), which corresponds to answer choice C: ln(98).