What is 8ln(cos^2(t))+8ln(1+tan^2(t)) ?

The solution to 8ln(cos^2(t))+8ln(1+tan^2(t)) is ln(sec^{16}(t)cos^{16}(t))

Popular >

simplify 8ln(cos^2(t))+8ln(1+tan^2(t))

simplify

8 ln (cos^{2} (t)) + 8 ln (1 + tan^{2} (t))

ln (sec^{16} (t) cos^{16} (t))

Solution steps

8 ln (cos^{2} (t)) + 8 ln (1 + tan^{2} (t))

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 ln (cos^{2} (t)) = ln (cos^{2} (t)^{8})

= ln (cos^{2} (t)^{8}) + 8 ln (tan^{2} (t) + 1)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 ln (tan^{2} (t) + 1) = ln ((tan^{2} (t) + 1)^{8})

= ln (cos^{2} (t)^{8}) + ln ((tan^{2} (t) + 1)^{8})

Apply log rule:

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

ln (cos^{2} (t)^{8}) + ln ((1 + tan^{2} (t))^{8}) = ln (cos^{2} (t)^{8} (tan^{2} (t) + 1)^{8})

= ln (cos^{2} (t)^{8} (tan^{2} (t) + 1)^{8})

Simplify

cos^{2} (t)^{8} (1 + tan^{2} (t))^{8} : sec^{16} (t) cos^{16} (t)

= ln (sec^{16} (t) cos^{16} (t))

lo g_{4} (9) - 2 lo g_{4} (5)

2 lo g_{6} (5 A) + lo g_{6} (B) + 7 lo g_{6} (C)

ln (t) + \frac{s ^{2}}{4 t ^{2}} + ln ((\frac{s}{t})^{\frac{1}{2}})

2 lo g_{10} (c) + 3 lo g_{10} (k)

lo g_{3} (3 x + 4) - 7 lo g_{9} (x^{2}) + 6 lo g_{3} (x)

What is 8ln(cos^2(t))+8ln(1+tan^2(t)) ?
The solution to 8ln(cos^2(t))+8ln(1+tan^2(t)) is ln(sec^{16}(t)cos^{16}(t))