Question

\[2^{-x^{2}} = 5\] use common log and two decimal place approx. in answer.

Answer 1

\[\log_{10}2^{-x ^{2}}=\log_{10}5 \]
\[-x ^{2}\log_{10}2=\log_{10}5 \]
\[-x ^{2}=\log_{10}5/\log_{10}2 \]

\[-x ^{2}=2.32\]\[x ^{2}=-2.32\]


\[x=\pm \sqrt{-2.32}\]
\[x=\pm i \sqrt{2.32}\]

\[x=\pm 1.52i\]

Answer 2

Thank you very much!

Answer 3

You're welcome

Answer 4

\[3^{-x ^{2}} = 7 \] use common log and two decimal place but why does book say "no solution" for this one?

Answer 5

You're right there can't be any complex numbers. They have to be real numbers for x. So there is no solution.

Thanks for the correction