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

Answer:

ln6 = 1.79

Step-by-step 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

$ln(a\times b)=ln(a)+ln(b)$

$6=3\times 2$

$ln6=ln(3\times 2)\\\Rightarrow ln6=ln3+ln2\\\Rightarrow ln6=1.10+0.69\\\Rightarrow ln6=1.79$

∴ ln6 = 1.79