Question

Which of the following is the solution of the equation?

Answer 1

Given that,

`5.2^(-3t)=45`

To find the solution of the above equation.

Dividing 5 on both sides,we get,

`\begin{gathered} 2^(-3t)=(45)/(5) \\ 2^(-3t)=9 \end{gathered}`

we know that,

`a^x=b\text{ if and only if }\log _ab=x`

we get,

`-3t=\log _29`
`t=-(1)/(3)\log _29`

Answer is: option(B):

`t=-(1)/(3)\log _29`