simplify ln(156e^5)

Solution

simplify

ln (156 e^{5})

ln (156) + 5

Decimal

10.04985 \dots

Solution steps

ln (156 e^{5})

Apply log rule:

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

ln (156 e^{5}) = ln (156) + ln (e^{5})

= ln (156) + ln (e^{5})

Apply log rule:

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

ln (e^{5}) = 5 ln (e)

= ln (156) + 5 ln (e)

5 ln (e) = 5

= ln (156) + 5

6 lo g_{c} (y) - \frac{1}{3} lo g_{c} (w) + 4 lo g_{c} (x)

ln (x^{2} - 9) - ln (3 + x)

ln (\frac{x ^{2}}{x ^{2} - 36})

- lo g_{10} (6.37 \cdot 1 0^{- 9})

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