What is 0.8+1.2*ln((48^2)/(33^2)) ?

The solution to 0.8+1.2*ln((48^2)/(33^2)) is 0.8+1.2(2ln(48)-2ln(33))

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simplify 0.8+1.2*ln((48^2)/(33^2))

simplify

0.8 + 1.2 \cdot ln (\frac{4 8 ^{2}}{3 3 ^{2}})

0.8 + 1.2 (2 ln (48) - 2 ln (33))

Decimal Notation

1.69926 \dots

Solution steps

0.8 + 1.2 ln (\frac{4 8 ^{2}}{3 3 ^{2}})

Apply log rule:

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

ln (\frac{4 8 ^{2}}{3 3 ^{2}}) = ln (4 8^{2}) - ln (3 3^{2})

= 0.8 + 1.2 (ln (4 8^{2}) - ln (3 3^{2}))

Apply log rule:

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

ln (4 8^{2}) = 2 ln (48)

= 0.8 + 1.2 (2 ln (48) - ln (3 3^{2}))

Apply log rule:

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

ln (3 3^{2}) = 2 ln (33)

= 0.8 + 1.2 (2 ln (48) - 2 ln (33))

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What is 0.8+1.2*ln((48^2)/(33^2)) ?
The solution to 0.8+1.2*ln((48^2)/(33^2)) is 0.8+1.2(2ln(48)-2ln(33))