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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 0.60611 \dots + πn

Degrees

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

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

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

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