What is ln(((0.132*10^{-3})(47*10^3))/(10)) ?

The solution to ln(((0.132*10^{-3})(47*10^3))/(10)) is -ln(10)+ln(47)+ln(0.132)

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simplify ln(((0.13210^{-3})(4710^3))/(10))

simplify

ln (\frac{( 0.132 \cdot 1 0 ^{- 3} ) ( 47 \cdot 1 0 ^{3} )}{10})

- ln (10) + ln (47) + ln (0.132)

Decimal Notation

- 0.47739 \dots

Solution steps

ln (\frac{( 0.132 \cdot 1 0 ^{- 3} ) ( 47 \cdot 1 0 ^{3} )}{10})

Apply log rule:

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

ln (\frac{( 0.132 \cdot 1 0 ^{- 3} ) ( 47 \cdot 1 0 ^{3} )}{10}) = ln ((0.132 \cdot 1 0^{- 3}) (47 \cdot 1 0^{3})) - ln (10)

= ln (1 0^{- 3} \cdot 1 0^{3} \cdot 47 \cdot 0.132) - ln (10)

Apply log rule:

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

ln (0.132 \cdot 1 0^{- 3} \cdot 47 \cdot 1 0^{3}) = ln (0.132) + ln (1 0^{- 3}) + ln (47) + ln (1 0^{3})

= ln (0.132) + ln (1 0^{- 3}) + ln (47) + ln (1 0^{3}) - ln (10)

Apply log rule:

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

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

= ln (0.132) - 3 ln (10) + ln (47) + ln (1 0^{3}) - ln (10)

Apply log rule:

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

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

= ln (0.132) - 3 ln (10) + ln (47) + 3 ln (10) - ln (10)

Group like terms

= - 3 ln (10) + 3 ln (10) - ln (10) + ln (47) + ln (0.132)

Add similar elements:

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

= - ln (10) + ln (47) + ln (0.132)

lo g_{8} (7 x^{4})

ln (x) + ln (x - 5)

lo g_{4} (\frac{x ^{2}}{y ^{2} z ^{7}})

4 (ln (3) - ln (2)) + 6 (ln (7) - ln (6))

2 ln (\frac{α q}{α + 1})

What is ln(((0.132*10^{-3})(47*10^3))/(10)) ?
The solution to ln(((0.132*10^{-3})(47*10^3))/(10)) is -ln(10)+ln(47)+ln(0.132)