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If 2^x = 25, what is 2^(x/2 + 3)?

 Oct 27, 2019
 #1
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I don't know if you are allowed to use a calculator or not, 

but,

we can find 2^x=25 (Find x by using logs)

\(log_2 25=x\)

x=4.644 approx. 

 

Plugging in x in the second expre.

2^(4.644/2+3) = 40 approx. 

 Oct 27, 2019
 #2
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to do this problem without a calculator:

 

\(2^x=25\)

\(log\)2\(25=x\)

\({1\over2}log\)2\(25=x/2\)

\(log\)2\(25^{1/2}=x/2\)

\(log\)2\(5=x/2\)

 

\(2^{x/2+3}\)

\(=2^{x/2}*2^3\)

\(=2^{log2(5)}*2^3\)

\(=5*2^3\)

\(=5*8\)

\(=40\)

 

So, the answer is exactly 40.

 Oct 27, 2019

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