What is the general solution for 0=e^{tan(x)}-2 ?

The general solution for 0=e^{tan(x)}-2 is x=0.60611…+pin

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0=e^{tan(x)}-2

0 = e^{t a n (x)} - 2

x = 0.60611 \dots + πn

Degrees

x = 34.72765 \dots^{\circ} + 18 0^{\circ} n

Solution steps

0 = e^{t a n (x)} - 2

Switch sides

e^{t a n (x)} - 2 = 0

Add

2

to both sides

e^{t a n (x)} - 2 + 2 = 0 + 2

Simplify

e^{t a n (x)} = 2

Apply exponent rules

e^{t a n (x)} = 2

f (x) = g (x)

, then

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

ln (e^{t a n (x)}) = ln (2)

Apply log rule:

ln (e^{a}) = a

ln (e^{t a n (x)}) = tan (x)

tan (x) = ln (2)

tan (x) = ln (2)

Apply trig inverse properties

tan (x) = ln (2)

General solutions for

tan (x) = ln (2)

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (ln (2)) + πn

x = arctan (ln (2)) + πn

Show solutions in decimal form

x = 0.60611 \dots + πn

cot (x) = \frac{3}{2}

4 tan^{2} (x) - 1 = 0

cos (\frac{2 x - 3}{2}) = - \frac{1}{2}

2 sin (θ) cos (θ) = cos (θ)

7 cos (x) = 5 cos (x) + 3

What is the general solution for 0=e^{tan(x)}-2 ?
The general solution for 0=e^{tan(x)}-2 is x=0.60611…+pin