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Solve for x: \(\Large 2^{2^x} = 16^{16^{16}}\)

 May 13, 2020
 #1
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2^(2^x) = 16 ^(16^16)

 

Take the log of both sides

 

log 2^(2^x)  = log(16)^(16^16)   and we can write

 

(2^x) log 2  =  (16^16)log 16

 

And we can write

 

2^x / (16^16)  = log 16/ log 2

 

2^x / 16^16  =  log 2^4  / log 2

 

2^x / 16^16  =  4 log 2 / log 2

 

2^x /  16^16  =  4    rearrange  as

 

2^x / 4  =  16^16

 

2^x / 2^2  = 16^16

 

2^ (x - 2) = (2^4)^16

 

2^(x - 2) = 2^(64)      we can solve for the exponents

 

x - 2   = 64

 

x   =  66

 

 

cool cool cool

 May 13, 2020

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