What is the general solution for 2^{tan(α)}= 1/4 ?

The general solution for 2^{tan(α)}= 1/4 is α=-1.10714…+pin

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2^{tan(α)}= 1/4

2^{t a n (α)} = \frac{1}{4}

α = - 1.10714 \dots + πn

Degrees

α = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2^{t a n (α)} = \frac{1}{4}

Apply exponent rules

2^{t a n (α)} = \frac{1}{4}

Convert to base

2 : 2^{t a n (α)} = 2^{- 2}

Convert

4

to base

2

4 = 2^{2}

2^{t a n (α)} = \frac{1}{2 ^{2}}

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{2 ^{2}} = 2^{- 2}

2^{t a n (α)} = 2^{- 2}

2^{t a n (α)} = 2^{- 2}

a^{f (x)} = a^{g (x)}

, then

f (x) = g (x)

tan (α) = - 2

tan (α) = - 2

Apply trig inverse properties

tan (α) = - 2

General solutions for

tan (α) = - 2

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

α = arctan (- 2) + πn

α = arctan (- 2) + πn

Show solutions in decimal form

α = - 1.10714 \dots + πn

tan^{4} (x) - 3 tan^{2} (x) + 1 = 0

tan (θ) = \frac{- 4}{- 1}

cos (2 x) - 7 cos (x) + 6 = 0

csc^{2} (x) = 2 + csc (x)

tan (θ) = \frac{5.4}{1.1}

What is the general solution for 2^{tan(α)}= 1/4 ?
The general solution for 2^{tan(α)}= 1/4 is α=-1.10714…+pin