What is ln((21)/(2x))-ln_{4}(21) ?

The solution to ln((21)/(2x))-ln_{4}(21) is ln(21)-ln(2)-ln(x)-ln_{4}(21)

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simplify ln((21)/(2x))-ln_{4}(21)

simplify

ln (\frac{21}{2 x}) - ln_{4} (21)

ln (21) - ln (2) - ln (x) - ln_{4} (21)

Solution steps

ln (\frac{21}{2 x}) - ln_{4} (21)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{21}{2 x}) = ln (21) - ln (2 x)

= ln (21) - ln (2 x) - ln_{4} (21)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 x) = ln (2) + ln (x)

= ln (21) - (ln (x) + ln (2)) - ln_{4} (21)

- (ln (2) + ln (x)) : - ln (2) - ln (x)

= ln (21) - ln (2) - ln (x) - ln_{4} (21)

\frac{1}{6} ln (\frac{x - 3}{x + 3})

ln (\frac{x}{5}) + \frac{x ^{2}}{25}

lo g_{3} (2 (ab)^{3} c)

- ln (x y) ln (x) + \frac{1}{2} ln^{2} (x) - 2 ln (x)

4 ln (t x) - 2 ln (\frac{x}{t ^{3}})

What is ln((21)/(2x))-ln_{4}(21) ?
The solution to ln((21)/(2x))-ln_{4}(21) is ln(21)-ln(2)-ln(x)-ln_{4}(21)