What is ln((6.09)/(9.42*10^{-3)}) ?

The solution to ln((6.09)/(9.42*10^{-3)}) is ln(6.09)-ln(9.42)+3ln(10)

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simplify ln((6.09)/(9.42*10^{-3)})

simplify

ln (\frac{6.09}{9.42 \cdot 1 0 ^{- 3}})

ln (6.09) - ln (9.42) + 3 ln (10)

Decimal Notation

6.47156 \dots

Solution steps

ln (\frac{6.09}{9.42 \cdot 1 0 ^{- 3}})

Apply log rule:

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

ln (\frac{6.09}{9.42 \cdot 1 0 ^{- 3}}) = ln (6.09) - ln (9.42 \cdot 1 0^{- 3})

= ln (6.09) - ln (1 0^{- 3} \cdot 9.42)

Apply log rule:

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

ln (9.42 \cdot 1 0^{- 3}) = ln (9.42) + ln (1 0^{- 3})

= ln (6.09) - (ln (9.42) + ln (1 0^{- 3}))

Apply log rule:

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

ln (1 0^{- 3}) = - 3 ln (10)

= ln (6.09) - (ln (9.42) - 3 ln (10))

- (ln (9.42) - 3 ln (10)) : - ln (9.42) + 3 ln (10)

= ln (6.09) - ln (9.42) + 3 ln (10)

- lo g_{10} (1.34 \cdot 1 0^{- 11})

0.01 \cdot lo g_{2} (0.01) + 0.99 \cdot lo g_{2} (0.99)

ln (x^{6} (x + 9)^{7} (x^{2} + 8)^{2})

96 - 10 \cdot lo g_{10} (\frac{4 \cdot 3.14 \cdot 4 ^{2}}{2})

ln ((- 0.34)^{23.2505} (- 0.86)^{7.84805})

What is ln((6.09)/(9.42*10^{-3)}) ?
The solution to ln((6.09)/(9.42*10^{-3)}) is ln(6.09)-ln(9.42)+3ln(10)