simplify ln(2(3)^x)

Solution

simplify

ln (2 (3)^{x})

ln (2) + x ln (3)

Solution steps

ln (2 (3)^{x})

Apply log rule:

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

ln (2 \cdot 3^{x}) = ln (2) + ln (3^{x})

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

Apply log rule:

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

ln (3^{x}) = x ln (3)

= ln (2) + x ln (3)

ln (\frac{1}{\frac{x c d}{d x}})

3.74 + lo g_{10} (\frac{1}{1.5})

- 6 ln ∣ x - 6 ∣ - 7 ln ∣ x + 2 ∣ - 3 ln ∣ x + 7 ∣ + C

- \frac{1}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1)