What is (ln(v)-2ln(cos(v)))/2 ?

The solution to (ln(v)-2ln(cos(v)))/2 is (ln(vsec^2(v)))/2

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simplify (ln(v)-2ln(cos(v)))/2

simplify

\frac{ln ( v ) - 2 ln ( cos ( v ) )}{2}

\frac{ln ( v sec ^{2} ( v ) )}{2}

Solution steps

\frac{ln ( v ) - 2 ln ( cos ( v ) )}{2}

Apply log rule:

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

2 ln (cos (v)) = ln (cos^{2} (v))

= \frac{ln ( v ) - ln ( cos ^{2} ( v ) )}{2}

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (v) - ln (cos^{2} (v)) = ln (\frac{v}{cos ^{2} ( v )})

= \frac{ln ( \frac{v}{c o s ^{2} ( v )} )}{2}

Rewrite using trig identities

= \frac{ln ( v sec ^{2} ( v ) )}{2}

60 ln (\frac{5.981}{1.711})

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2 lo g_{3} (A) - 3 lo g_{3} (B)

What is (ln(v)-2ln(cos(v)))/2 ?
The solution to (ln(v)-2ln(cos(v)))/2 is (ln(vsec^2(v)))/2