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

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

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

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

x = 0.60611 \dots + πn

Solution steps

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

tan (x) = ln (2)

Apply trig inverse properties

x = arctan (ln (2)) + πn

Show solutions in decimal form

x = 0.60611 \dots + πn

32 sec (θ) + 7 = 1

cos (x) + cos^{2} (x) - sin^{2} (x) = 0

x, 2 sin (x) + csc (x) = 0

4 cos^{2} (x) + 4 = 6

sin (2 x + \frac{π}{6}) = - \frac{1}{2}

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