What is 0.6ln(1372.5)+0.6ln(1647) ?

The solution to 0.6ln(1372.5)+0.6ln(1647) is ln(6494.16877…)

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simplify 0.6ln(1372.5)+0.6ln(1647)

simplify

0.6 ln (1372.5) + 0.6 ln (1647)

ln (6494.16877 \dots)

Decimal Notation

8.77865 \dots

Solution steps

0.6 ln (1372.5) + 0.6 ln (1647)

Apply log rule:

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

0.6 ln (1372.5) = ln (1372. 5^{0.6})

= ln (1372. 5^{0.6}) + 0.6 ln (1647)

Apply log rule:

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

0.6 ln (1647) = ln (164 7^{0.6})

= ln (1372. 5^{0.6}) + ln (164 7^{0.6})

Apply log rule:

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

ln (1372. 5^{0.6}) + ln (164 7^{0.6}) = ln (164 7^{0.6} \cdot 1372. 5^{0.6})

= ln (164 7^{0.6} \cdot 1372. 5^{0.6})

1372. 5^{0.6} \cdot 164 7^{0.6} = 6494.16877 \dots

= ln (6494.16877 \dots)

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What is 0.6ln(1372.5)+0.6ln(1647) ?
The solution to 0.6ln(1372.5)+0.6ln(1647) is ln(6494.16877…)