What is ln(((1.6*10^{-19}))/((6.48*10^{-5))}) ?

The solution to ln(((1.6*10^{-19}))/((6.48*10^{-5))}) is -14ln(10)+ln(1.6)-ln(6.48)

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simplify ln(((1.610^{-19}))/((6.4810^{-5))})

simplify

ln (\frac{( 1.6 \cdot 1 0 ^{- 19} )}{( 6.48 \cdot 1 0 ^{- 5} )})

- 14 ln (10) + ln (1.6) - ln (6.48)

Decimal Notation

- 33.63490 \dots

Solution steps

ln (\frac{( 1.6 \cdot 1 0 ^{- 19} )}{( 6.48 \cdot 1 0 ^{- 5} )})

Apply log rule:

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

ln (\frac{( 1.6 \cdot 1 0 ^{- 19} )}{( 6.48 \cdot 1 0 ^{- 5} )}) = ln ((1.6 \cdot 1 0^{- 19})) - ln ((6.48 \cdot 1 0^{- 5}))

= ln (1 0^{- 19} \cdot 1.6) - ln (1 0^{- 5} \cdot 6.48)

Apply log rule:

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

ln (1.6 \cdot 1 0^{- 19}) = ln (1.6) + ln (1 0^{- 19}), ln (6.48 \cdot 1 0^{- 5}) = ln (6.48) + ln (1 0^{- 5})

= ln (1.6) + ln (1 0^{- 19}) - (ln (6.48) + ln (1 0^{- 5}))

Apply log rule:

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

ln (1 0^{- 19}) = - 19 ln (10)

= ln (1.6) - 19 ln (10) - (ln (6.48) + ln (1 0^{- 5}))

Apply log rule:

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

ln (1 0^{- 5}) = - 5 ln (10)

= ln (1.6) - 19 ln (10) - (ln (6.48) - 5 ln (10))

- (ln (6.48) - 5 ln (10)) : - ln (6.48) + 5 ln (10)

= ln (1.6) - 19 ln (10) - ln (6.48) + 5 ln (10)

Simplify

ln (1.6) - 19 ln (10) - ln (6.48) + 5 ln (10) : - 14 ln (10) + ln (1.6) - ln (6.48)

= - 14 ln (10) + ln (1.6) - ln (6.48)

lo g_{10} (2) + \frac{1}{2} \cdot lo g_{10} (15) - \frac{1}{4} \cdot lo g_{10} (9)

lo g_{b} (x^{7} y^{3} z)

- 2 ln ∣ 4 - 1 ∣ + 3 ln ∣ 4 - 2 ∣ + ln 4^{2} + 1 + 2 - ln (\frac{5}{2})

lo g_{2} (5) + lo g_{2} (x^{3})

lo g_{5} (\frac{x ^{11}}{x - 7})

What is ln(((1.6*10^{-19}))/((6.48*10^{-5))}) ?
The solution to ln(((1.6*10^{-19}))/((6.48*10^{-5))}) is -14ln(10)+ln(1.6)-ln(6.48)