Solve Exponential Equation For x

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IMG_20220313_214219.jpg
 
2^(sin^2(x)) +2^(cos^2(x)) = 3...........2^x =3 for x = log(3)/log(2)=>2^( log(3)/log(2))=3

2^(sin^2(x)) +2^(cos^2(x)) = 2^( log(3)/log(2)).........bases are same, exponents must be same too
sin^2(x) +cos^2(x) = log(3)/log(2)
1 = 3.....................(no solutions exist)


but, if x=0 equation is true

2^(sin^2(0)) +2^(cos^2(0)) = 3..........true

or if you write it in this form
upload_2022-3-14_13-2-4.gif
you also have x ≈ -37.6991118430775

upload_2022-3-14_13-3-30.gif
.......true
 
2^(sin^2(x)) +2^(cos^2(x)) = 3...........2^x =3 for x = log(3)/log(2)=>2^( log(3)/log(2))=3

2^(sin^2(x)) +2^(cos^2(x)) = 2^( log(3)/log(2)).........bases are same, exponents must be same too
sin^2(x) +cos^2(x) = log(3)/log(2)
1 = 3.....................(no solutions exist)


but, if x=0 equation is true

2^(sin^2(0)) +2^(cos^2(0)) = 3..........true

or if you write it in this form
View attachment 2224 you also have x ≈ -37.6991118430775

View attachment 2225 .......true

Excellent.

Try this one:

Solve Trigonometric System
 

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