Question

solve the following exponential equation by expressing each side as a power of the same base and then equating exponents:
81^x=1/(square root of 3)

Answer 1

\[81 = 3^4\]\[\frac{1}{\sqrt{3}} = 3^{-\frac{1}{2}}\]\[81^x = \frac{1}{\sqrt{3}}\]\[\left( 3^{4} \right)^x= 3^{-\frac{1}{2}}\]\[3^{4x} = 3^{-\frac{1}{2}}\]