simplify ln(7*e^x)

Solution

simplify

ln (7 \cdot e^{x})

ln (7) + x

Solution steps

ln (7 e^{x})

Apply log rule:

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

ln (7 e^{x}) = ln (7) + ln (e^{x})

= ln (7) + ln (e^{x})

Apply log rule:

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

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

= ln (7) + x ln (e)

x ln (e) = x

= ln (7) + x

f (x) = 4 [ln (x) - ln (x + 3) - ln (x - 3)]

f (x) = lo g_{3} (2 x) - lo g_{3} (x)

f (x) = lo g_{x} (2 \cdot 7)

ln (\frac{z ^{3}}{x y})

f (z) = lo g_{10} (3 z) + 2 lo g_{10} (7)