What is ln(3)(-1-1/2-1/8+3/4)+ln(2)(1-1/4-3/4) ?

The solution to ln(3)(-1-1/2-1/8+3/4)+ln(2)(1-1/4-3/4) is ln((\sqrt[8]{3})/3)

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simplify ln(3)(-1-1/2-1/8+3/4)+ln(2)(1-1/4-3/4)

simplify

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

Decimal Notation

- 0.96128 \dots

Solution steps

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

Apply log rule:

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

ln (3) (\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8}) = ln (3^{(\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8})})

= ln (3^{(\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8})}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

Apply log rule:

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

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

= ln (3^{(\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8})}) + ln (2^{(1 - \frac{1}{4} - \frac{3}{4})})

Apply log rule:

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

ln (3^{(- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4})}) + ln (2^{(1 - \frac{1}{4} - \frac{3}{4})}) = ln (3^{\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8}} \cdot 2^{1 - \frac{1}{4} - \frac{3}{4}})

= ln (3^{\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8}} \cdot 2^{1 - \frac{1}{4} - \frac{3}{4}})

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

lo g_{10} (5 x) - lo g_{10} (4 y)

lo g_{b} (\frac{x ^{2}}{y ^{3} z ^{4}})

3 lo g_{7} (x) + \frac{1}{3} lo g_{7} (y)

- lo g_{10} (3.4 \cdot 1 0^{- 2})

What is ln(3)(-1-1/2-1/8+3/4)+ln(2)(1-1/4-3/4) ?
The solution to ln(3)(-1-1/2-1/8+3/4)+ln(2)(1-1/4-3/4) is ln((\sqrt[8]{3})/3)