Answer:
Given that,
[tex]5.2^{-3t}=45[/tex]
To find the solution of the above equation.
Dividing 5 on both sides,we get,
[tex]\begin{gathered} 2^{-3t}=\frac{45}{5} \\ 2^{-3t}=9 \end{gathered}[/tex]
we know that,
[tex]a^x=b\text{ if and only if }\log _ab=x[/tex]
we get,
[tex]-3t=\log _29[/tex][tex]t=-\frac{1}{3}\log _29[/tex]
Answer is: option(B):
[tex]t=-\frac{1}{3}\log _29[/tex]
