simplify ln(5e^6)

Solution

simplify

ln (5 e^{6})

ln (5) + 6

Solution steps

ln (5 e^{6})

Apply log rule:

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

ln (5 e^{6}) = ln (5) + ln (e^{6})

= ln (5) + ln (e^{6})

Apply log rule:

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

ln (e^{6}) = 6 ln (e)

= ln (5) + 6 ln (e)

6 ln (e) = 6

= ln (5) + 6

- \frac{1}{4} lo g_{2} (\frac{1}{4}) - \frac{3}{4} lo g_{2} (\frac{3}{4})

ln (5 e^{x})

\frac{1}{7} [lo g_{10} (x) - lo g_{10} (x + 4)]

lo g_{6} (1296 x)

3 lo g_{4} (x^{2}) + \frac{1}{2} lo g_{4} (x)