What is ln(1/(16e^2)) ?

The solution to ln(1/(16e^2)) is -(4ln(2)+2)

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simplify ln(1/(16e^2))

simplify

ln (\frac{1}{16 e ^{2}})

- (4 ln (2) + 2)

Decimal Notation

- 4.77258 \dots

Solution steps

ln (\frac{1}{16 e ^{2}})

Apply log rule:

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

ln (\frac{1}{16 e ^{2}}) = ln (1) - ln (16 e^{2})

= ln (1) - ln (16 e^{2})

Apply log rule:

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

ln (16 e^{2}) = ln (16) + ln (e^{2})

= ln (1) - (ln (16) + ln (e^{2}))

Apply log rule:

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

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

= ln (1) - (ln (16) + 2 ln (e))

ln (1) = 0

- (ln (16) + 2 ln (e)) = - (4 ln (2) + 2)

= 0 - (4 ln (2) + 2)

0 - (4 ln (2) + 2) = - (4 ln (2) + 2)

= - (4 ln (2) + 2)

10 lo g_{10} (x) - 2 lo g_{10} (x^{2})

lo g_{10} (\frac{c}{a ^{4} b ^{4}})

lo g_{10} (5 x y^{2})

lo g_{10} (\frac{y}{1})

lo g_{6} (\frac{x}{y})