What is the general solution for tan(3^x)=0 ?

The general solution for tan(3^x)=0 is x=(ln(pin))/(ln(3))

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tan(3^x)=0

tan (3^{x}) = 0

x = \frac{ln ( πn )}{ln ( 3 )}

Degrees

x = 0^{\circ} + 59.70094 \dots^{\circ} n

Solution steps

tan (3^{x}) = 0

General solutions for

tan (3^{x}) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

3^{x} = 0 + πn

3^{x} = 0 + πn

Solve

3^{x} = 0 + πn : x = \frac{ln ( πn )}{ln ( 3 )}

3^{x} = 0 + πn

Apply exponent rules

3^{x} = 0 + πn

f (x) = g (x)

, then

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

ln (3^{x}) = ln (0 + πn)

Apply log rule:

ln (x^{a}) = a \cdot ln (x)

ln (3^{x}) = x ln (3)

x ln (3) = ln (0 + πn)

x ln (3) = ln (0 + πn)

Solve

x ln (3) = ln (0 + πn) : x = \frac{ln ( πn )}{ln ( 3 )}

x ln (3) = ln (0 + πn)

0 + πn = πn

x ln (3) = ln (πn)

Divide both sides by

ln (3)

x ln (3) = ln (πn)

Divide both sides by

ln (3)

\frac{x ln ( 3 )}{ln ( 3 )} = \frac{ln ( πn )}{ln ( 3 )}

Simplify

x = \frac{ln ( πn )}{ln ( 3 )}

x = \frac{ln ( πn )}{ln ( 3 )}

x = \frac{ln ( πn )}{ln ( 3 )}

x = \frac{ln ( πn )}{ln ( 3 )}

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

tan^{2} (x) + 5 tan (x) - 7 = 0

sin (x) = \frac{- 3}{4}

cot^{2} (x) - 3 cot (x) = 0

tan (θ) = 2

What is the general solution for tan(3^x)=0 ?
The general solution for tan(3^x)=0 is x=(ln(pin))/(ln(3))