simplify ln(3e^2x)

Solution

simplify

ln (3 e^{2} x)

ln (3) + 2 + ln (x)

Solution steps

ln (3 e^{2} x)

Apply log rule:

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

ln (3 e^{2} x) = ln (3) + ln (e^{2}) + ln (x)

= ln (3) + ln (e^{2}) + ln (x)

Apply log rule:

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

ln (e^{2}) = 2 ln (e)

= ln (3) + 2 ln (e) + ln (x)

2 ln (e) = 2

= ln (3) + 2 + ln (x)

- 30 ln (\frac{ln ( 0.0066 )}{ln ( 2 )})

ln (- 0.00507 (24))

ln ∣ p ∣ - ln ∣ p + 1000000 ∣

(\frac{1}{3} ln ∣ e^{x} + 1 ∣ + \frac{2}{3} ln ∣ e^{x} - 2 ∣) \cdot e^{x}

- \frac{1}{0.43861} ln (\frac{5}{1205})