What is 9ln(cos^2(t))+9ln(1+tan^2(t)) ?

The solution to 9ln(cos^2(t))+9ln(1+tan^2(t)) is ln(sec^{18}(t)cos^{18}(t))

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simplify 9ln(cos^2(t))+9ln(1+tan^2(t))

simplify

9 ln (cos^{2} (t)) + 9 ln (1 + tan^{2} (t))

ln (sec^{18} (t) cos^{18} (t))

Solution steps

9 ln (cos^{2} (t)) + 9 ln (1 + tan^{2} (t))

Apply log rule:

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

9 ln (cos^{2} (t)) = ln (cos^{2} (t)^{9})

= ln (cos^{2} (t)^{9}) + 9 ln (tan^{2} (t) + 1)

Apply log rule:

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

9 ln (tan^{2} (t) + 1) = ln ((tan^{2} (t) + 1)^{9})

= ln (cos^{2} (t)^{9}) + ln ((tan^{2} (t) + 1)^{9})

Apply log rule:

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

ln (cos^{2} (t)^{9}) + ln ((1 + tan^{2} (t))^{9}) = ln (cos^{2} (t)^{9} (tan^{2} (t) + 1)^{9})

= ln (cos^{2} (t)^{9} (tan^{2} (t) + 1)^{9})

Simplify

cos^{2} (t)^{9} (1 + tan^{2} (t))^{9} : sec^{18} (t) cos^{18} (t)

= ln (sec^{18} (t) cos^{18} (t))

lo g_{3} (5) + lo g_{3} (8) - lo g_{3} (2)

lo g_{3} (9 x^{4})

3 \cdot lo g_{10} (2) + 2 \cdot lo g_{10} (3)

- 0.8 lo g_{2} (0.8) - 0.2 lo g_{2} (0.2)

lo g_{10} (5 x + 4) - lo g_{10} (x)

What is 9ln(cos^2(t))+9ln(1+tan^2(t)) ?
The solution to 9ln(cos^2(t))+9ln(1+tan^2(t)) is ln(sec^{18}(t)cos^{18}(t))