What is simplify-12ln(8)+12ln(4) ?

The solution to simplify-12ln(8)+12ln(4) is -12ln(2)

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simplify-12ln(8)+12ln(4)

simplify

- 12 ln (8) + 12 ln (4)

- 12 ln (2)

Decimal Notation

- 8.31776 \dots

Solution steps

- 12 ln (8) + 12 ln (4)

Apply log rule:

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

12 ln (8) = ln (8^{12})

= - ln (8^{12}) + 12 ln (4)

Apply log rule:

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

12 ln (4) = ln (4^{12})

= - ln (8^{12}) + ln (4^{12})

Apply log rule:

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

ln (4^{12}) - ln (8^{12}) = ln (\frac{4 ^{12}}{8 ^{12}})

= ln (\frac{4 ^{12}}{8 ^{12}})

\frac{4 ^{12}}{8 ^{12}} = \frac{1}{4096}

= ln (\frac{1}{4096})

Apply log rule:

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

= - ln (4096)

Rewrite

4096

in power-base form:

4096 = 2^{12}

= - ln (2^{12})

Apply log rule:

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

ln (2^{12}) = 12 ln (2)

= - 12 ln (2)

- \frac{3}{4} lo g_{2} (\frac{3}{4}) - \frac{1}{4} lo g_{10} (x)

(\frac{1}{0.143}) ln (\frac{5 \cdot 1 0 ^{9}}{34000})

\frac{300}{2 \cdot π \cdot 450} \cdot ln (\frac{4 + 2 \cdot 45 0 ^{2}}{25})

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

- lo g_{10} (4.61 \cdot 1 0^{- 7})

What is simplify-12ln(8)+12ln(4) ?
The solution to simplify-12ln(8)+12ln(4) is -12ln(2)