simplify ln(t^2xy)

Solution

simplify

ln (t^{2} x y)

2 ln (t) + ln (x) + ln (y)

Solution steps

ln (t^{2} x y)

Apply log rule:

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

ln (t^{2} x y) = ln (t^{2}) + ln (x) + ln (y)

= ln (t^{2}) + ln (x) + ln (y)

Apply log rule:

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

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

= 2 ln (t) + ln (x) + ln (y)

ln (x) - 2 ln (z) - \frac{1}{6} ln (y)

lo g_{4} ((3 x yz)^{2})

6^{\frac{7 l o g _{6} ( 2 )}{2}} + 1

lo g_{10} ((\frac{7}{8})^{x})

ln (\frac{2}{sin ( θ )}) - ln (\frac{1}{sin ( θ )})