What is ln((ln(x^2))/(4x)) ?

The solution to ln((ln(x^2))/(4x)) is ln(ln(x))-ln(x)-ln(2)

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simplify ln((ln(x^2))/(4x))

simplify

ln (\frac{ln ( x ^{2} )}{4 x})

ln (ln (x)) - ln (x) - ln (2)

Solution steps

ln (\frac{ln ( x ^{2} )}{4 x})

Apply log rule:

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

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

= ln (ln (x^{2})) - ln (4 x)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

= ln (2 ln (x)) - ln (4 x)

Apply log rule:

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

ln (2 ln (x)) = ln (2) + ln (ln (x)), ln (4 x) = ln (4) + ln (x)

= ln (2) + ln (ln (x)) - (ln (x) + ln (4))

ln (4) = 2 ln (2)

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

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

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

Simplify

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

= ln (ln (x)) - ln (x) - ln (2)

ln (\frac{( 48 ) - ( 9 )}{( 70 ) - ( 9 )})

ln (\frac{658405861}{2405861})

ln (2) - ln (\frac{3}{3})

ln (7) + ln (x) + 5 ln (y) - 2 ln (x)

ln ((x + 5)^{2} \cdot x)

What is ln((ln(x^2))/(4x)) ?
The solution to ln((ln(x^2))/(4x)) is ln(ln(x))-ln(x)-ln(2)