Question

Use logarithmic properties and the fact that ln(2) ≈ 0.69 and ln(3) ≈ 1.10 to approximate the value of each of the following logarithmic expressions. Do not use a calculator.

ln(6)

Answer 1

ln6 = 1.79

Explanation:

The logarithm here has base e so it is a natural logarithm.

`log_ex=lnx`

`lnx=y\\\Rightarrow e^y=x`

According to the product rule of logarithms

`ln(a* b)=ln(a)+ln(b)`

`6=3* 2`

`ln6=ln(3* 2)\\\Rightarrow ln6=ln3+ln2\\\Rightarrow ln6=1.10+0.69\\\Rightarrow ln6=1.79`

∴ ln6 = 1.79