What is ln(7)-2(ln(4)+ln(32)) ?

The solution to ln(7)-2(ln(4)+ln(32)) is ln(7/16384)

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simplify ln(7)-2(ln(4)+ln(32))

simplify

ln (7) - 2 (ln (4) + ln (32))

ln (\frac{7}{16384})

Decimal Notation

- 7.75815 \dots

Solution steps

ln (7) - 2 (ln (4) + ln (32))

Apply log rule:

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

ln (4) + ln (32) = ln (4 \cdot 32)

= ln (7) - 2 ln (4 \cdot 32)

Multiply the numbers:

4 \cdot 32 = 128

= ln (7) - 2 ln (128)

Apply log rule:

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

2 ln (128) = ln (12 8^{2})

= ln (7) - ln (12 8^{2})

Apply log rule:

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

ln (7) - ln (12 8^{2}) = ln (\frac{7}{12 8 ^{2}})

= ln (\frac{7}{12 8 ^{2}})

12 8^{2} = 16384

= ln (\frac{7}{16384})

3 ln (\frac{5.5}{5})

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- ln (\frac{1 - a}{a})

\frac{1}{2} ln (\frac{1 + \frac{3}{2}}{1 - \frac{3}{2}})

What is ln(7)-2(ln(4)+ln(32)) ?
The solution to ln(7)-2(ln(4)+ln(32)) is ln(7/16384)