Answer :
Given:
The function is:
[tex]f(x)=1822.8(1.4^x)[/tex]Find-:
Value of "x." when f(x) is 406500000000
Explanation-:
The value of "x" is:
[tex]\begin{gathered} f(x)=1822.8(1.4^x) \\ \\ f(x)=406500000000 \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} 1822.8(1.4)^x=406500000000 \\ \\ 1.4^x=\frac{4065\times10^8}{1822.8} \\ \\ 1.4^x=2.23\times10^8 \end{gathered}[/tex]Taking log both sides then,
[tex]\begin{gathered} \log_.1.4^x=\log_.2.23\times10^8 \\ \\ x=\frac{\log_.2.23\times10^8}{\log_.1.4} \\ \\ x=\frac{8.348}{0.146} \\ \\ x=57.13 \end{gathered}[/tex]The value of "x" is 57.13