simplify ln(5*10^4)

Solution

simplify

ln (5 \cdot 1 0^{4})

ln (5) + 4 ln (10)

Decimal Notation

10.81977 \dots

Solution steps

ln (5 \cdot 1 0^{4})

Apply log rule:

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

ln (5 \cdot 1 0^{4}) = ln (5) + ln (1 0^{4})

= ln (5) + 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)

= ln (5) + 4 ln (10)

- ln \frac{v}{v - c} + ln \frac{v}{v + c}

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ln (4 x y)

ln (\frac{373}{283})

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