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If x is a real number such that 2^{2x-5}=18, find 2^x.

 Nov 17, 2020
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2^(2x - 5)  =  18      

 

2^(2x)/ 2^5  = 18

 

(4)^x  = 2^5 * 18

 

4^x  = 576       lake the log of log of  both sides

 

log 4^x  = log 576

 

x * log 4  = log 576

 

x = log 576 / log 4

 

2^x =  2^ ( log 576 / log 4)  =   24

 

 

cool cool cool 

 Nov 17, 2020
edited by CPhill  Nov 17, 2020

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