simplify ln(ie^pi)

Solution

simplify

ln (i e^{π})

ln (i) + π

Solution steps

ln (i e^{π})

Apply log rule:

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

ln (i e^{π}) = ln (i) + ln (e^{π})

= ln (i) + ln (e^{π})

Apply log rule:

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

ln (e^{π}) = π ln (e)

= ln (i) + π ln (e)

π ln (e) = π

= ln (i) + π

- ln ∣ 8 - 3 ∣ + 2 ln ∣ 8 - 2 ∣

\frac{1}{14} \cdot ln (129)

ln (\frac{3}{11})

2 lo g_{10} (x) + 7 lo g_{10} (x - 9)

1.005 \cdot ln (1.687) - 0.287 \cdot ln (4.5)