Question

please show steps: Solve:
log base 5 3-1/2 log base 5 x=log base 5 1/2

Answer 1

use log identities:
http://en.wikipedia.org/wiki/Logarithm#Product.2C_quotient.2C_power_and_root

\[\log_{5}3 - \frac{1}{2}\log_{5} x = \log_{5} \frac{1}{2} \]
\[\log_{5}3 - \log_{5} \sqrt{x} = \log_{5} \frac{1}{2}\]
\[\log_{5} \frac{3}{\sqrt{x}} = \log_{5} \frac{1}{2}\]
\[\frac{3}{\sqrt{x}} = \frac{1}{2}\]
\[\sqrt{x} = 6\]
\[x = 36\]