What is ln(1x10^{-3}) ?

The solution to ln(1x10^{-3}) is ln(x)-3ln(10)

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simplify ln(1x10^{-3})

simplify

ln (1 x 1 0^{- 3})

ln (x) - 3 ln (10)

Solution steps

ln (1 \cdot x \cdot 1 0^{- 3})

Apply log rule:

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

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

= ln (1) + ln (x) + 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 (1) + ln (x) - 3 ln (10)

Apply log rule:

lo g_{a} (1) = 0

= 0 + ln (x) - 3 ln (10)

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

= ln (x) - 3 ln (10)

ln (b \cdot e^{2})

ln (a + b) + 4 ln (a - b) - 5 ln (c)

\frac{ln ( 80 ) - ln ( 10 )}{- 0.004}

- 3 lo g_{2} (x) - 2 lo g_{2} (y)

ln (\frac{1}{2}) + ln (1)