What is ln((1.4)/1)+3ln((1.8)/(1.4)) ?

The solution to ln((1.4)/1)+3ln((1.8)/(1.4)) is ln(2.97551…)

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simplify ln((1.4)/1)+3ln((1.8)/(1.4))

simplify

ln (\frac{1.4}{1}) + 3 ln (\frac{1.8}{1.4})

ln (2.97551 \dots)

Decimal Notation

1.09041 \dots

Solution steps

ln (\frac{1.4}{1}) + 3 ln (\frac{1.8}{1.4})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (\frac{1.8}{1.4}) = ln ((\frac{1.8}{1.4})^{3})

= ln (\frac{1.4}{1}) + ln ((\frac{1.8}{1.4})^{3})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{1.4}{1}) + ln ((\frac{1.8}{1.4})^{3}) = ln (\frac{1.4}{1} (\frac{1.8}{1.4})^{3})

= ln (\frac{1.4}{1} (\frac{1.8}{1.4})^{3})

\frac{1.4}{1} (\frac{1.8}{1.4})^{3} = 2.97551 \dots

= ln (2.97551 \dots)

ln (\frac{0.015}{1.5})

ln (K R) - ln (K)

- [10 (ln (2) - ln (0.1)) + 5 (2 - 0.1)]

ln (7) x - ln (7) - 2 ln (4)

0.3 5^{2} (ln (6.65) + 1.3 (ln (6.01) - ln (6.65)))

What is ln((1.4)/1)+3ln((1.8)/(1.4)) ?
The solution to ln((1.4)/1)+3ln((1.8)/(1.4)) is ln(2.97551…)