What is expand log_{8}((4sqrt(5))/6) ?

The solution to expand log_{8}((4sqrt(5))/6) is 2/3+1/2 log_{8}(5)-log_{8}(6)

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expand log_{8}((4sqrt(5))/6)

expand

lo g_{8} (\frac{4 5}{6})

\frac{2}{3} + \frac{1}{2} lo g_{8} (5) - lo g_{8} (6)

Decimal Notation

0.19200 \dots

Solution steps

lo g_{8} (\frac{4 5}{6})

Apply log rule:

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

lo g_{8} (\frac{4 5}{6}) = lo g_{8} (45) - lo g_{8} (6)

= lo g_{8} (45) - lo g_{8} (6)

Apply log rule:

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

lo g_{8} (45) = lo g_{8} (4) + lo g_{8} (5)

= lo g_{8} (4) + lo g_{8} (5) - lo g_{8} (6)

lo g_{8} (5) = \frac{1}{2} lo g_{8} (5)

= lo g_{8} (4) + \frac{1}{2} lo g_{8} (5) - lo g_{8} (6)

lo g_{8} (4) = \frac{2}{3}

= \frac{2}{3} + \frac{1}{2} lo g_{8} (5) - lo g_{8} (6)

6 ln (x) + 4 ln (y) - 3 ln (z)

lo g_{10} (\frac{a ^{2} ab}{( ab ) ^{2}})

2 lo g_{10} (x) - 8 lo g_{10} (y)

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

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

What is expand log_{8}((4sqrt(5))/6) ?
The solution to expand log_{8}((4sqrt(5))/6) is 2/3+1/2 log_{8}(5)-log_{8}(6)