What is ln(13)-2(ln(4)+ln(32)) ?

The solution to ln(13)-2(ln(4)+ln(32)) is ln(13/16384)

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simplify ln(13)-2(ln(4)+ln(32))

simplify

ln (13) - 2 (ln (4) + ln (32))

ln (\frac{13}{16384})

Decimal Notation

- 7.13911 \dots

Solution steps

ln (13) - 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 (13) - 2 ln (4 \cdot 32)

Multiply the numbers:

4 \cdot 32 = 128

= ln (13) - 2 ln (128)

Apply log rule:

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

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

= ln (13) - ln (12 8^{2})

Apply log rule:

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

ln (13) - ln (12 8^{2}) = ln (\frac{13}{12 8 ^{2}})

= ln (\frac{13}{12 8 ^{2}})

12 8^{2} = 16384

= ln (\frac{13}{16384})

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

lo g_{a} (3 x^{2}) - 2 lo g_{a} (x)

lo g_{a} (5) + lo g_{a} (4)

ln (\frac{4}{k})

0.02 ln (\frac{8}{3})

What is ln(13)-2(ln(4)+ln(32)) ?
The solution to ln(13)-2(ln(4)+ln(32)) is ln(13/16384)