What is expand log_{8}(a^6b^5) ?

The solution to expand log_{8}(a^6b^5) is 6log_{8}(a)+5log_{8}(b)

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expand log_{8}(a^6b^5)

expand

lo g_{8} (a^{6} b^{5})

6 lo g_{8} (a) + 5 lo g_{8} (b)

Solution steps

lo g_{8} (a^{6} b^{5})

Apply log rule:

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

lo g_{8} (a^{6} b^{5}) = lo g_{8} (a^{6}) + lo g_{8} (b^{5})

= lo g_{8} (a^{6}) + lo g_{8} (b^{5})

Apply log rule:

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

lo g_{8} (a^{6}) = 6 lo g_{8} (a)

= 6 lo g_{8} (a) + lo g_{8} (b^{5})

Apply log rule:

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

lo g_{8} (b^{5}) = 5 lo g_{8} (b)

= 6 lo g_{8} (a) + 5 lo g_{8} (b)

ln (\frac{67}{7})

ln (2 e^{x})

ln (\frac{e ^{3}}{5})

- lo g_{10} (1.3 \cdot 1 0^{- 3})

What is expand log_{8}(a^6b^5) ?
The solution to expand log_{8}(a^6b^5) is 6log_{8}(a)+5log_{8}(b)