simplify ln(b^2e^x)

Solution

simplify

ln (b^{2} e^{x})

2 ln (b) + x

Solution steps

ln (b^{2} e^{x})

Apply log rule:

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

ln (b^{2} e^{x}) = ln (b^{2}) + ln (e^{x})

= ln (b^{2}) + ln (e^{x})

Apply log rule:

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

ln (b^{2}) = 2 ln (b)

= 2 ln (b) + ln (e^{x})

Apply log rule:

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

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

= 2 ln (b) + x ln (e)

x ln (e) = x

= 2 ln (b) + x

ln (x) - ln (4)

4 ln (2) - ln (3)

- lo g_{10} (\frac{0.021}{0.018} \cdot 2.3 \cdot 1 0^{- 11})

ln (y - 3) - ln (y - 1)

- a^{2} ln (x) - 2 ln (x - a) + ln (x + a)