$[-/5\mathrm{.}55$ Points$]$

LARCALC$125\mathrm{.}5\mathrm{.}085.$

Consider the function $f(x)=lo{g}_7(x).$

$($a$)$ What is the domain of $f?($Enter your answer using interval notation.$)$

$($b$)$ Find $f^{-1}.$

$f^{-1}(x)=$

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$($c$)$ Let $x$ be a real number between $343$ and $2,401.$ Determine the interval in which $f(x)$ will be found. $($Enter your answer using interval notation.$)$

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$($d$)$ Determine the interval in which $x$ will be found if $f(x)$ is negative. $($Enter your answer using interval notation.$)$

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$($e$)$ When $f(x)$ is increased by one unit, $x$ must have been increased by what factor?

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$($f$)$ Find the ratio of $x_1$ to $x_2$ given that $f(x_1)=3n$ and $f(x_2)=n.$

$\frac{x_1}{x_2}=$

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