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Popular >

solvefor x,Rf=e^{cos(2x)}

Solution

solve for

x, R f = e^{c o s (2 x)}

Solution

x = \frac{arccos ( ln ( R f ) )}{2} + πn, x = - \frac{arccos ( ln ( R f ) )}{2} + πn

Solution steps

R f = e^{c o s (2 x)}

Switch sides

e^{c o s (2 x)} = R f

Apply exponent rules

e^{c o s (2 x)} = R f

If

f (x) = g (x)

, then

ln (f (x)) = ln (g (x))

ln (e^{c o s (2 x)}) = ln (R f)

Apply log rule:

ln (e^{a}) = a

ln (e^{c o s (2 x)}) = cos (2 x)

cos (2 x) = ln (R f)

cos (2 x) = ln (R f)

Apply trig inverse properties

cos (2 x) = ln (R f)

General solutions for

cos (2 x) = ln (R f)

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

2 x = arccos (ln (R f)) + 2 πn, 2 x = - arccos (ln (R f)) + 2 πn

2 x = arccos (ln (R f)) + 2 πn, 2 x = - arccos (ln (R f)) + 2 πn

Solve

2 x = arccos (ln (R f)) + 2 πn : x = \frac{arccos ( ln ( R f ) )}{2} + πn

2 x = arccos (ln (R f)) + 2 πn

Divide both sides by

2

2 x = arccos (ln (R f)) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( ln ( R f ) )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( ln ( R f ) )}{2} + πn

x = \frac{arccos ( ln ( R f ) )}{2} + πn

Solve

2 x = - arccos (ln (R f)) + 2 πn : x = - \frac{arccos ( ln ( R f ) )}{2} + πn

2 x = - arccos (ln (R f)) + 2 πn

Divide both sides by

2

2 x = - arccos (ln (R f)) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arccos ( ln ( R f ) )}{2} + \frac{2 πn}{2}

Simplify

x = - \frac{arccos ( ln ( R f ) )}{2} + πn

x = - \frac{arccos ( ln ( R f ) )}{2} + πn

x = \frac{arccos ( ln ( R f ) )}{2} + πn, x = - \frac{arccos ( ln ( R f ) )}{2} + πn

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