What is ln((7.28*10^{-4})/(1.93*10^{-7)}) ?

The solution to ln((7.28*10^{-4})/(1.93*10^{-7)}) is 3ln(10)+ln(7.28)-ln(1.93)

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simplify ln((7.2810^{-4})/(1.9310^{-7)})

simplify

ln (\frac{7.28 \cdot 1 0 ^{- 4}}{1.93 \cdot 1 0 ^{- 7}})

3 ln (10) + ln (7.28) - ln (1.93)

Decimal Notation

8.23536 \dots

Solution steps

ln (\frac{7.28 \cdot 1 0 ^{- 4}}{1.93 \cdot 1 0 ^{- 7}})

Apply log rule:

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

ln (\frac{7.28 \cdot 1 0 ^{- 4}}{1.93 \cdot 1 0 ^{- 7}}) = ln (7.28 \cdot 1 0^{- 4}) - ln (1.93 \cdot 1 0^{- 7})

= ln (1 0^{- 4} \cdot 7.28) - ln (1 0^{- 7} \cdot 1.93)

Apply log rule:

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

ln (7.28 \cdot 1 0^{- 4}) = ln (7.28) + ln (1 0^{- 4}), ln (1.93 \cdot 1 0^{- 7}) = ln (1.93) + ln (1 0^{- 7})

= ln (7.28) + ln (1 0^{- 4}) - (ln (1.93) + ln (1 0^{- 7}))

Apply log rule:

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

ln (1 0^{- 4}) = - 4 ln (10)

= ln (7.28) - 4 ln (10) - (ln (1.93) + ln (1 0^{- 7}))

Apply log rule:

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

ln (1 0^{- 7}) = - 7 ln (10)

= ln (7.28) - 4 ln (10) - (ln (1.93) - 7 ln (10))

- (ln (1.93) - 7 ln (10)) : - ln (1.93) + 7 ln (10)

= ln (7.28) - 4 ln (10) - ln (1.93) + 7 ln (10)

Simplify

ln (7.28) - 4 ln (10) - ln (1.93) + 7 ln (10) : 3 ln (10) + ln (7.28) - ln (1.93)

= 3 ln (10) + ln (7.28) - ln (1.93)

2 lo g_{10} (a) + 3 lo g_{10} (b) - lo g_{10} (c)

\frac{1}{3} lo g_{10} (27) - \frac{1}{2} lo g_{10} (49)

ln ((2) e^{7 b})

\frac{( \frac{- 6 l n ^{3} ( 2 ) + 13 l n ^{2} ( 2 ) + 18 l n ( x ) + 12}{16 l n ^{5} ( 2 )} )}{120}

lo g_{10} (310 z)

What is ln((7.28*10^{-4})/(1.93*10^{-7)}) ?
The solution to ln((7.28*10^{-4})/(1.93*10^{-7)}) is 3ln(10)+ln(7.28)-ln(1.93)