What is simplify-3ln(13)+3ln(18) ?

The solution to simplify-3ln(13)+3ln(18) is ln(5832/2197)

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simplify-3ln(13)+3ln(18)

simplify

- 3 ln (13) + 3 ln (18)

ln (\frac{5832}{2197})

Decimal Notation

0.97626 \dots

Solution steps

- 3 ln (13) + 3 ln (18)

Apply log rule:

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

3 ln (13) = ln (1 3^{3})

= - ln (1 3^{3}) + 3 ln (18)

Apply log rule:

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

3 ln (18) = ln (1 8^{3})

= - ln (1 3^{3}) + ln (1 8^{3})

Apply log rule:

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

ln (1 8^{3}) - ln (1 3^{3}) = ln (\frac{1 8 ^{3}}{1 3 ^{3}})

= ln (\frac{1 8 ^{3}}{1 3 ^{3}})

\frac{1 8 ^{3}}{1 3 ^{3}} = \frac{5832}{2197}

= ln (\frac{5832}{2197})

ln (92) - ln (x)

- 0.67 lo g_{2} (0.67) - 0.33 lo g_{2} (0.33)

0.491 \cdot ln (22) - 0.491 \cdot ln (20)

- \frac{5 ln ( 0.905 ) - ln ( \frac{45}{367} )}{0.85 ln ( 0.905 )}

0.799 - 0.05916 lo g_{10} (\frac{1}{3.1 \cdot 1 0 ^{- 8}})

What is simplify-3ln(13)+3ln(18) ?
The solution to simplify-3ln(13)+3ln(18) is ln(5832/2197)