What is ln(2ln(2))-ln(ln(2)) ?

The solution to ln(2ln(2))-ln(ln(2)) is ln(2)

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simplify ln(2ln(2))-ln(ln(2))

simplify

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

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

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

Apply log rule:

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

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

= ln (\frac{2 ln ( 2 )}{ln ( 2 )})

Cancel the common factor:

ln (2)

= ln (2)

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lo g_{10} (\frac{y ^{2}}{2 z})