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

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.

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.