What is expand log_{8}((12^6)/(7^2)) ?

The solution to expand log_{8}((12^6)/(7^2)) is 6log_{8}(12)-2log_{8}(7)

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expand log_{8}((12^6)/(7^2))

expand

lo g_{8} (\frac{1 2 ^{6}}{7 ^{2}})

6 lo g_{8} (12) - 2 lo g_{8} (7)

Decimal Notation

5.29835 \dots

Solution steps

lo g_{8} (\frac{1 2 ^{6}}{7 ^{2}})

Apply log rule:

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

lo g_{8} (\frac{1 2 ^{6}}{7 ^{2}}) = lo g_{8} (1 2^{6}) - lo g_{8} (7^{2})

= lo g_{8} (1 2^{6}) - lo g_{8} (7^{2})

Apply log rule:

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

lo g_{8} (1 2^{6}) = 6 lo g_{8} (12)

= 6 lo g_{8} (12) - lo g_{8} (7^{2})

Apply log rule:

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

lo g_{8} (7^{2}) = 2 lo g_{8} (7)

= 6 lo g_{8} (12) - 2 lo g_{8} (7)

ln (5) + 2 ln (x) + 3 (x^{2} + 5)

\frac{28}{0.693} \cdot ln (\frac{100}{9})

ln (6 (ln (x) - 5))

5 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

\frac{33}{10} ln (6)

What is expand log_{8}((12^6)/(7^2)) ?
The solution to expand log_{8}((12^6)/(7^2)) is 6log_{8}(12)-2log_{8}(7)