What is ln((3(1)^2)/(2-1)) ?

The solution to ln((3(1)^2)/(2-1)) is ln(3)

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simplify ln((3(1)^2)/(2-1))

simplify

ln (\frac{3 ( 1 ) ^{2}}{2 - 1})

ln (3)

Decimal Notation

1.09861 \dots

Solution steps

ln (\frac{3 ( 1 ) ^{2}}{2 - 1})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{3 \cdot 1 ^{2}}{2 - 1}) = ln (3 \cdot 1^{2}) - ln (2 - 1)

= ln (1^{2} \cdot 3) - ln (2 - 1)

Apply log rule:

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

ln (3 \cdot 1^{2}) = ln (3) + ln (1^{2})

= ln (3) + ln (1^{2}) - ln (2 - 1)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1^{2}) = 2 ln (1)

= ln (3) + 2 ln (1) - ln (2 - 1)

2 ln (1) = 0

ln (2 - 1) = 0

= ln (3) + 0 - 0

0 - 0 = 0

= ln (3)

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