The simplified expression is In (25x). Option D shows the simplified expression of the given equation.
The given expression is,
[tex]In \; x + 2 In \; 5 + In \; 1[/tex]
We will use the basic properties of the logarithm to simply the given expression.
The Basic Properties of Logs are,
[tex]log_b(xy) = log_b\;x + log_b\;y.[/tex]
[tex]log_b(x/y) = log_b\;x - log_b\;y.[/tex]
[tex]log_b(xn) = n log_b\;x.[/tex]
[tex]log_b\;x = log_a\;x / log_a\;b.[/tex]
[tex]log \;1= 0[/tex]
By using 3rd and 5th property, we simply the given expression as,
[tex]In\; x + In \; 5^2 + 0[/tex]
[tex]In \; x + In \; 25[/tex]
By using the first property, we get the expression,
[tex]In \; x + In \; 25[/tex]
[tex]In \; (x \times 25)[/tex]
[tex]In \;25x[/tex]
Hence the simplified expression is In (25x). Option D shows the simplified expression of the given equation.
To know more about the logarithm, follow the link given below.
https://brainly.com/question/5956809.
