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.
