simplify ln(6*10^6)

Solution

simplify

ln (6 \cdot 1 0^{6})

ln (6) + 6 ln (10)

Decimal

15.60727 \dots

Solution steps

ln (6 \cdot 1 0^{6})

Apply log rule:

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

ln (6 \cdot 1 0^{6}) = ln (6) + ln (1 0^{6})

= ln (6) + ln (1 0^{6})

Apply log rule:

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

ln (1 0^{6}) = 6 ln (10)

= ln (6) + 6 ln (10)

ln (a) - 5 ln (b) + 3 ln (c)

ln (\frac{2 3}{3})

6 ln (x - 5) - ln (x^{2} - 8 x + 15) + 2 ln (x - 3)

2 ln (x - 3) - ln (6) - 3 ln (x + 2)

\frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x + 2 ∣