What is ln(1)+ln(15)+ln(120)+ln(680) ?

The solution to ln(1)+ln(15)+ln(120)+ln(680) is ln(680)+ln(1800)

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simplify ln(1)+ln(15)+ln(120)+ln(680)

simplify

ln (1) + ln (15) + ln (120) + ln (680)

ln (680) + ln (1800)

Decimal Notation

14.01763 \dots

Solution steps

ln (1) + ln (15) + ln (120) + ln (680)

Apply log rule:

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

ln (15) + ln (120) = ln (15 \cdot 120)

= ln (1) + ln (15 \cdot 120) + ln (680)

Multiply the numbers:

15 \cdot 120 = 1800

= ln (1) + ln (1800) + ln (680)

Apply log rule:

lo g_{a} (1) = 0

= 0 + ln (1800) + ln (680)

0 + ln (1800) + ln (680) = ln (1800) + ln (680)

= ln (680) + ln (1800)

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ln (1 + sin (x)) - ln (1 - sin (x))

What is ln(1)+ln(15)+ln(120)+ln(680) ?
The solution to ln(1)+ln(15)+ln(120)+ln(680) is ln(680)+ln(1800)