What is 2ln(3)+ln(2)-(ln(6))/(ln(e)) ?

The solution to 2ln(3)+ln(2)-(ln(6))/(ln(e)) is ln(18)-ln(6)

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simplify 2ln(3)+ln(2)-(ln(6))/(ln(e))

simplify

2 ln (3) + ln (2) - \frac{ln ( 6 )}{ln ( e )}

ln (18) - ln (6)

Decimal Notation

1.09861 \dots

Solution steps

2 ln (3) + ln (2) - \frac{ln ( 6 )}{ln ( e )}

Apply log rule:

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

2 ln (3) = ln (3^{2})

= ln (3^{2}) + ln (2) - \frac{ln ( 6 )}{ln ( e )}

Apply log rule:

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

ln (3^{2}) + ln (2) = ln (3^{2} \cdot 2)

= ln (3^{2} \cdot 2) - \frac{ln ( 6 )}{ln ( e )}

3^{2} \cdot 2 = 18

= ln (18) - \frac{ln ( 6 )}{ln ( e )}

\frac{ln ( 6 )}{ln ( e )} = ln (6)

= ln (18) - ln (6)

lo g_{5} (\frac{a ^{3}}{b ^{2}})

ln (4 e^{6})

lo g_{10} (2 x - 7) - lo g_{10} (x - 1)

lo g_{b} (\frac{p ^{4} q ^{7}}{m ^{4} b ^{7}})

2 ln (5) + ln (6)

What is 2ln(3)+ln(2)-(ln(6))/(ln(e)) ?
The solution to 2ln(3)+ln(2)-(ln(6))/(ln(e)) is ln(18)-ln(6)