Final answer:
The natural logarithm of 1/5, denoted as ln(1/5), is approximately -1.6094. When rounded to the nearest tenth, it is -1.6.
Step-by-step explanation:
To find the value of ln(1/5), we can use a calculator. The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is approximately 2.71828. When we input 1/5 into the natural logarithm function, we get a negative value because the input is less than 1.
Using the natural logarithm rule ln(a/b) = ln(a) - ln(b), we can break down ln(1/5) into ln(1) - ln(5). Since ln(1) is 0, we simply need to find ln(5) and then change the sign. Most calculators will show ln(5) as approximately 1.6094, so ln(1/5) would be -1.6094.
To round this to the nearest tenth, we look at the first digit after the decimal we are considering, which is the hundredths place in this case. Since the digit is 0 (<5), we do not round up. Therefore, ln(1/5) rounded to the nearest tenth is -1.6.