use the approximations ln 2=0.693 and ln= 1.609 together with the properties of natural logarithms to calculate an approximation to ln 40
40=2^3*5
ln(40)=3ln(2)+ln(5)
Can you take it from here?
To approximate ln 40 using the given approximations of ln 2 and ln 10, you can apply the properties of logarithms.
First, note that ln 40 = ln (2 * 20). Using the property ln (a * b) = ln a + ln b, we can write:
ln 40 = ln 2 + ln 20
Now, let's break down ln 20 further. We can write ln 20 = ln (2 * 10). Again, using the property ln (a * b) = ln a + ln b:
ln 20 = ln 2 + ln 10
Now, substitute the given approximations:
ln 40 ≈ ln 2 + ln 20 ≈ 0.693 + 1.609
Calculating this sum approximately, we get:
ln 40 ≈ 2.302
Therefore, an approximation for ln 40 using the given approximations is ln 40 ≈ 2.302.