Answer:
\(x=\frac{3}{16}\)
Step-by-step explanation:
Given : Exponential function \(9^{8x}=27\)
We have to solve the given exponential equation.
Consider the given exponential function \(9^{8x}=27\)
\(\mathrm{Convert\:}9^{8x}\mathrm{\:to\:base\:}3\)
\(9^{8x}=\left(3^2\right)^{8x}\)
Function becomes,
\(\left(3^2\right)^{8x}=27\)
Convert 27 to base 3, we have,
\(\left(3^2\right)^{8x}=3^3\)
Apply exponent rule, \(\left(a^b\right)^c=a^{bc}\)
We have, \(3^{2\cdot \:8x}=3^3\)
\(\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)\)
We have,
\(2\cdot \:8x=3\)
Simplify, we have,
\(16x=3\)
Thus, \(x=\frac{3}{16}\)
