What is ln(3)-2(ln(4)+ln(32)) ?

The solution to ln(3)-2(ln(4)+ln(32)) is ln(3/16384)

Popular >

simplify ln(3)-2(ln(4)+ln(32))

simplify

ln (3) - 2 (ln (4) + ln (32))

ln (\frac{3}{16384})

Decimal Notation

- 8.60544 \dots

Solution steps

ln (3) - 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 (3) - 2 ln (4 \cdot 32)

Multiply the numbers:

4 \cdot 32 = 128

= ln (3) - 2 ln (128)

Apply log rule:

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

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

= ln (3) - ln (12 8^{2})

Apply log rule:

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

ln (3) - ln (12 8^{2}) = ln (\frac{3}{12 8 ^{2}})

= ln (\frac{3}{12 8 ^{2}})

12 8^{2} = 16384

= ln (\frac{3}{16384})

lo g_{10} (\frac{1}{2}) + lo g_{10} (\frac{2}{3})

ln (x - 1 (2 x - 3)^{\frac{1}{4}})

lo g_{b} (a^{5} b^{4})

lo g_{5} (100) + lo g_{5} (4)

What is ln(3)-2(ln(4)+ln(32)) ?
The solution to ln(3)-2(ln(4)+ln(32)) is ln(3/16384)