simplify ln(e^5x)

Solution

simplify

ln (e^{5} x)

5 + ln (x)

Solution steps

ln (e^{5} x)

Apply log rule:

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

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

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

Apply log rule:

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

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

= 5 ln (e) + ln (x)

5 ln (e) = 5

= 5 + ln (x)

lo g_{8} ((\frac{x ^{3} y}{2})^{2})

- lo g_{10} (4.15 \cdot 1 0^{- 3})

ln (f (6.01))

0.0259 \cdot ln (\frac{1 0 ^{15}}{1.5 \cdot 1 0 ^{10}})

lo g_{10} (x) + 2 lo g_{10} (y) + 3