What is expand log_{8}((x^3)/5) ?

The solution to expand log_{8}((x^3)/5) is 3log_{8}(x)-log_{8}(5)

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expand log_{8}((x^3)/5)

expand

lo g_{8} (\frac{x ^{3}}{5})

3 lo g_{8} (x) - lo g_{8} (5)

Solution steps

lo g_{8} (\frac{x ^{3}}{5})

Apply log rule:

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

lo g_{8} (\frac{x ^{3}}{5}) = lo g_{8} (x^{3}) - lo g_{8} (5)

= lo g_{8} (x^{3}) - lo g_{8} (5)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{8} (x^{3}) = 3 lo g_{8} (x)

= 3 lo g_{8} (x) - lo g_{8} (5)

lo g_{10} (x) + lo g_{10} (x + 3) - 2 lo g_{10} (x + 1)

- \frac{1}{3} + \frac{1}{3} ln (\frac{3 + 5}{2})

3 ln (2) - 2 ln (3)

\frac{6 ln ( 3 ) - 10 ln ( 2 )}{2}

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

What is expand log_{8}((x^3)/5) ?
The solution to expand log_{8}((x^3)/5) is 3log_{8}(x)-log_{8}(5)