Step-by-step solution:

The given expression is:

7+\log_{3}{4x}=9

Collect the like term:

\log_{3}{4x}=9-7

After subtraction we get,

\log_{3}{4x}=2

We know that:

\log_{a}{b}=c \implies {b}=a^c

similarly,

\log_{3}{4x}=2\implies {4x}=3^2

After solving we get:

4x=9\implies {x=\frac{9}{4}}

The required value of **x** is:

x=\frac{9}{4}

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