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Question

The domain of the function $f left parenthesis x right parenthesis equals log subscript 2 invisible function application open parentheses log subscript 3 invisible function application open parentheses log subscript 4 invisible function application x close parentheses close parentheses$ is

$(- \infty, 4)$
$(4, \infty)$
$(0, 4)$
$(1, \infty)$

The correct answer is: $left parenthesis 4 comma straight infinity right parenthesis$

Given, $f left parenthesis x right parenthesis equals log subscript 2 invisible function application open parentheses log subscript 3 invisible function application open parentheses log subscript 4 invisible function application x close parentheses close parentheses$
We know, $log subscript a invisible function application x$ is defined, if $x greater than 0$
For $f left parenthesis x right parenthesis$ to be defined.
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell log subscript 3 invisible function application log subscript 4 invisible function application x greater than 0 comma log subscript 4 invisible function application x greater than 0 text and end text x greater than 0 end cell row cell not stretchy rightwards double arrow log subscript 4 invisible function application x greater than 3 to the power of 0 equals 1 comma x greater than 4 to the power of 0 equals 1 text and end text x greater than 0 end cell row cell not stretchy rightwards double arrow x greater than 4 comma x greater than 1 text and end text x greater than 0 end cell row cell not stretchy rightwards double arrow x greater than 4 end cell end table$

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parallel

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parallel

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parallel

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