What is 2.4ln(3)+2.4ln(2) ?

The solution to 2.4ln(3)+2.4ln(2) is ln(73.71621…)

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simplify 2.4ln(3)+2.4ln(2)

simplify

2.4 ln (3) + 2.4 ln (2)

ln (73.71621 \dots)

Decimal Notation

4.30022 \dots

Solution steps

2.4 ln (3) + 2.4 ln (2)

Apply log rule:

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

2.4 ln (3) = ln (3^{2.4})

= ln (3^{2.4}) + 2.4 ln (2)

Apply log rule:

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

2.4 ln (2) = ln (2^{2.4})

= ln (3^{2.4}) + ln (2^{2.4})

Apply log rule:

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

ln (3^{2.4}) + ln (2^{2.4}) = ln (3^{2.4} \cdot 2^{2.4})

= ln (3^{2.4} \cdot 2^{2.4})

3^{2.4} \cdot 2^{2.4} = 73.71621 \dots

= ln (73.71621 \dots)

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