What is ln(5)+ln(7)+2ln(6) ?

The solution to ln(5)+ln(7)+2ln(6) is ln(1260)

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simplify ln(5)+ln(7)+2ln(6)

simplify

ln (5) + ln (7) + 2 ln (6)

ln (1260)

Decimal Notation

7.13886 \dots

Solution steps

ln (5) + ln (7) + 2 ln (6)

Apply log rule:

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

ln (5) + ln (7) = ln (5 \cdot 7)

= ln (5 \cdot 7) + 2 ln (6)

Multiply the numbers:

5 \cdot 7 = 35

= ln (35) + 2 ln (6)

Apply log rule:

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

2 ln (6) = ln (6^{2})

= ln (35) + ln (6^{2})

Apply log rule:

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

ln (35) + ln (6^{2}) = ln (6^{2} \cdot 35)

= ln (6^{2} \cdot 35)

35 \cdot 6^{2} = 1260

= ln (1260)

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