What is the general solution for solvefor y,arctan(y/x)=ln(x) ?

The general solution for solvefor y,arctan(y/x)=ln(x) is y=tan(ln(x))x

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solvefor y,arctan(y/x)=ln(x)

solve for

y, arctan (\frac{y}{x}) = ln (x)

y = tan (ln (x)) x

Solution steps

arctan (\frac{y}{x}) = ln (x)

Subtract

ln (x)

from both sides

arctan (\frac{y}{x}) - ln (x) = 0

Let:

u = \frac{y}{x}

arctan (u) - ln (x) = 0

Move

ln (x)

to the right side

arctan (u) - ln (x) = 0

Add

ln (x)

to both sides

arctan (u) - ln (x) + ln (x) = 0 + ln (x)

Simplify

arctan (u) = ln (x)

arctan (u) = ln (x)

Apply trig inverse properties

arctan (u) = ln (x)

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

u = tan (ln (x))

u = tan (ln (x))

Substitute back

u = \frac{y}{x}

\frac{y}{x} = tan (ln (x)) : y = tan (ln (x)) x; x \neq = 0

\frac{y}{x} = tan (ln (x))

Multiply both sides by

x

\frac{y}{x} = tan (ln (x))

Multiply both sides by

x

\frac{y x}{x} = tan (ln (x)) x; x \neq = 0

Simplify

y = tan (ln (x)) x; x \neq = 0

y = tan (ln (x)) x; x \neq = 0

y = tan (ln (x)) x

- cos (7 4^{\circ}) = cos (θ)

sin (x) = 50

58. 2^{2} = 25. 8^{2} + 33. 4^{2} - 2 (25.8 (33.4)) cos (a)

tan (θ) = - 3, 0 \leq θ \leq 2 π

4 cos (θ) - 1 = 2 sin (θ) tan (θ)

What is the general solution for solvefor y,arctan(y/x)=ln(x) ?
The general solution for solvefor y,arctan(y/x)=ln(x) is y=tan(ln(x))x