What is ln((2.1x10^{-4}x)/(0.9025)) ?

The solution to ln((2.1x10^{-4}x)/(0.9025)) is 2ln(x)+ln(2.1)-ln(0.9025)-4ln(10)

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simplify ln((2.1x10^{-4}x)/(0.9025))

simplify

ln (\frac{2.1 x 1 0 ^{- 4} x}{0.9025})

2 ln (x) + ln (2.1) - ln (0.9025) - 4 ln (10)

Solution steps

ln (\frac{2.1 x \cdot 1 0 ^{- 4} x}{0.9025})

Apply log rule:

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

ln (\frac{2.1 x \cdot 1 0 ^{- 4} x}{0.9025}) = ln (2.1 x \cdot 1 0^{- 4} x) - ln (0.9025)

= ln (1 0^{- 4} \cdot 2.1 xx) - ln (0.9025)

Apply log rule:

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

ln (2.1 x \cdot 1 0^{- 4} x) = ln (2.1) + ln (x) + ln (1 0^{- 4}) + ln (x)

= ln (2.1) + ln (x) + ln (1 0^{- 4}) + ln (x) - ln (0.9025)

Simplify

ln (2.1) + ln (x) + ln (1 0^{- 4}) + ln (x) - ln (0.9025) : 2 ln (x) + ln (2.1) - ln (0.9025) + ln (1 0^{- 4})

Apply log rule:

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

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

= 2 ln (x) + ln (2.1) - ln (0.9025) - 4 ln (10)

\frac{1}{398} ln (\frac{250}{238})

9.25 + lo g_{10} (\frac{0.18}{0.26})

- lo g_{10} (4 \cdot 1 0^{- 15})

8.314 (59 + 273) ln (0.286) - ln (1.99 \cdot 1 0^{11})

- lo g_{10} (7.2 \cdot 1 0^{- 5})

What is ln((2.1x10^{-4}x)/(0.9025)) ?
The solution to ln((2.1x10^{-4}x)/(0.9025)) is 2ln(x)+ln(2.1)-ln(0.9025)-4ln(10)