simplify ln(3e^5)

Solution

simplify

ln (3 e^{5})

ln (3) + 5

Decimal Notation

6.09861 \dots

Solution steps

ln (3 e^{5})

Apply log rule:

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

ln (3 e^{5}) = ln (3) + ln (e^{5})

= ln (3) + ln (e^{5})

Apply log rule:

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

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

= ln (3) + 5 ln (e)

5 ln (e) = 5

= ln (3) + 5

lo g_{4} (\frac{y}{( x + 1 ) ^{2}})

5 ln (x) + 2 ln (y) - 3 ln (z)

lo g_{10} (\frac{y}{z ^{5}})

lo g_{10} (\frac{4 x}{3})

lo g_{6} (x^{2} - 36) - lo g_{6} (x - 6)