What is ln((sqrt(6.1*7.36))/(9.42*10^{-3)}) ?

The solution to ln((sqrt(6.1*7.36))/(9.42*10^{-3)}) is 1/2 ln(44.896)-ln(9.42)+3ln(10)

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simplify ln((sqrt(6.17.36))/(9.4210^{-3)})

simplify

ln (\frac{6.1 \cdot 7.36}{9.42 \cdot 1 0 ^{- 3}})

\frac{1}{2} ln (44.896) - ln (9.42) + 3 ln (10)

Decimal Notation

6.56709 \dots

Solution steps

ln (\frac{6.1 \cdot 7.36}{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{6.1 \cdot 7.36}{9.42 \cdot 1 0 ^{- 3}}) = ln (6.1 \cdot 7.36) - ln (9.42 \cdot 1 0^{- 3})

= ln (6.1 \cdot 7.36) - 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 (6.1 \cdot 7.36) - (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 (6.1 \cdot 7.36) - (ln (9.42) - 3 ln (10))

ln (6.1 \cdot 7.36) = \frac{1}{2} ln (44.896)

= \frac{1}{2} ln (44.896) - (ln (9.42) - 3 ln (10))

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

= \frac{1}{2} ln (44.896) - ln (9.42) + 3 ln (10)

4 lo g_{10} (x) + 2 lo g_{10} (x - 1)

\frac{5 ln ( - 1 )}{6} - 3 \frac{1}{3}

\frac{1}{5} (6 ln (5) - ln (2))

ln (8) + ln (25)

ln (20 t)

What is ln((sqrt(6.1*7.36))/(9.42*10^{-3)}) ?
The solution to ln((sqrt(6.1*7.36))/(9.42*10^{-3)}) is 1/2 ln(44.896)-ln(9.42)+3ln(10)