What is simplify-8ln(4)+8ln(sqrt(8)) ?

The solution to simplify-8ln(4)+8ln(sqrt(8)) is -4ln(2)

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simplify-8ln(4)+8ln(sqrt(8))

simplify

- 8 ln (4) + 8 ln (8)

- 4 ln (2)

Decimal Notation

- 2.77258 \dots

Solution steps

- 8 ln (4) + 8 ln (8)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 ln (4) = ln (4^{8})

= - ln (4^{8}) + 8 ln (8)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 ln (8) = ln ((8)^{8})

= - ln (4^{8}) + ln ((8)^{8})

Apply log rule:

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

ln ((8)^{8}) - ln (4^{8}) = ln (\frac{( 8 ) ^{8}}{4 ^{8}})

= ln (\frac{( 8 ) ^{8}}{4 ^{8}})

\frac{( 8 ) ^{8}}{4 ^{8}} = \frac{1}{16}

= ln (\frac{1}{16})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (16)

Rewrite

16

in power-base form:

16 = 2^{4}

= - ln (2^{4})

Apply log rule:

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

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

= - 4 ln (2)

237.3 \cdot ln (\frac{11.11}{6.11})

ln ∣ x ∣ + \frac{3}{2} ln x^{2} + 6

\frac{57}{40} + \frac{5}{4} ln (\frac{4}{5}) + \frac{3}{8} ln (2)

lo g_{7} (\frac{1 + 2 e ^{- x}}{e ^{2 x}})

ln ((24 e^{- x - y})^{5}) + ln ((15 e^{3 x - y})^{3})

What is simplify-8ln(4)+8ln(sqrt(8)) ?
The solution to simplify-8ln(4)+8ln(sqrt(8)) is -4ln(2)