simplify ln(4e^3x)

Solution

simplify

ln (4 e^{3} x)

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

Solution steps

ln (4 e^{3} x)

Apply log rule:

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

ln (4 e^{3} x) = ln (4) + ln (e^{3}) + ln (x)

= ln (4) + ln (e^{3}) + ln (x)

Apply log rule:

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

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

= ln (4) + 3 ln (e) + ln (x)

3 ln (e) = 3

= ln (4) + 3 + ln (x)

ln (4) = 2 ln (2)

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

ln (3 x^{4} y^{6})

- 2 \cdot ln (\frac{0.2}{1.2})

\frac{ln ( 7 ) - ln ( 1.02 )}{3 ln ( 1.02 )}

6 ln (3) - 6 ln (2)

lo g_{e} (8) + 9 lo g_{e} (π) - lo g_{e} (5)