What is the general solution for 7=e^{2sin(x)}+3 ?

The general solution for 7=e^{2sin(x)}+3 is x=0.76584…+2pin,x=pi-0.76584…+2pin

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7=e^{2sin(x)}+3

7 = e^{2 s i n (x)} + 3

x = 0.76584 \dots + 2 πn, x = π - 0.76584 \dots + 2 πn

Solution steps

7 = e^{2 s i n (x)} + 3

Switch sides

e^{2 s i n (x)} + 3 = 7

Move

3

to the right side

e^{2 s i n (x)} = 4

Apply exponent rules

2 sin (x) = ln (4)

Solve

2 sin (x) = ln (4) : sin (x) = ln (2)

sin (x) = ln (2)

Apply trig inverse properties

x = arcsin (ln (2)) + 2 πn, x = π - arcsin (ln (2)) + 2 πn

Show solutions in decimal form

x = 0.76584 \dots + 2 πn, x = π - 0.76584 \dots + 2 πn

sin (u) = - 0.9

- \frac{3}{2} = - \frac{1}{2} sec (x)

sin (3 x + 1) = \frac{1}{2}

cos (x) = \frac{1 3 ^{2} + 1 8 ^{2} - 2 8 ^{2}}{2 \cdot 13 \cdot 18}

0.16085 = sin (\frac{2 π}{365} (x - 114))

What is the general solution for 7=e^{2sin(x)}+3 ?
The general solution for 7=e^{2sin(x)}+3 is x=0.76584…+2pin,x=pi-0.76584…+2pin