simplify ln(1/23)

Solution

simplify

ln (\frac{1}{23})

- ln (23)

Decimal Notation

- 3.13549 \dots

Solution steps

ln (\frac{1}{23})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{23}) = ln (1) - ln (23)

= ln (1) - ln (23)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (23)

0 - ln (23) = - ln (23)

= - ln (23)

9 \cdot ln (8) - ln (2!) + 7 \cdot ln (2) - ln (7!) - 3 \cdot 8

3 lo g_{b} (z) + 2 (lo g_{b} (y) - 5 lo g_{b} (x))

- \frac{( 8.314 \cdot 298 )}{96485} ln (\frac{0.002}{4})

lo g_{\frac{1}{2}} (\frac{1}{80})

4.74 + lo g_{10} (\frac{0.1}{0.175})