Natural Log LN (a^1/b^3c^-1)

Question

if a=2. b=3 c=5

evaluate the following. Give your answer as an integer, fraction, or decimal rounded to at least 4 places. 

Ln(a¹/b³c^-1)

Answer 1

Question: If a=2, b=3, and c=5, evaluate the following. Give your answer as an integer, fraction, or decimal rounded to at least 4 places. 

ln(a¹/b³c^-1)

Answer: Remember the rules of working with logarithms.

Let's take care of a big part first. Remember the Quotient Rule: ln(x/y) = ln(x) - ln(y)

ln(a¹/b³c^-1) = ln(a¹) - ln(b³c^-1)

Let's take care of another big part. Remember the Product Rule: ln(x*y) = ln(x) + ln(y)

ln(b³c^-1) = ln(b³) + ln(c^-1)

So now we have this expansion:

ln(a¹/b³c^-1) = ln(a¹) - [ ln(b³) + ln(c^-1) ]

Let's make some substitutions:

ln((2)¹) - [ ln((3)³) + ln((5)^-1) ]

Simplify. You will use the same rules as above, but in reverse, so please get to know them! They will be your best friend moving forward in math!

ln(2) - [ ln(27) + ln(1/5)]

ln(2) - [ ln(27*(1/5)) ]

ln(2) - ln(27/5)

ln( 2 / (27/5) )

ln(10/27)

So ln(10/27) is an exact final answer, but let's turn it into a decimal number rounded to four places.

Since the argument for the natural log is a fraction between 0 and 1, I expect the final number to be negative.

ln(10/27) ≈ -0.9933

Answer 2

ln (a¹ / b³c^-1)

ln (a¹c¹ / b³)

ln (2¹5¹ / 3³)

ln 10 / 27

ln 10 - ln 27

Can you finish and answer?