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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