What is log_{6}((36-4)/(216^3)) ?

The solution to log_{6}((36-4)/(216^3)) is 5log_{6}(2)-9

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simplify log_{6}((36-4)/(216^3))

simplify

lo g_{6} (\frac{36 - 4}{21 6 ^{3}})

5 lo g_{6} (2) - 9

Decimal Notation

- 7.06573 \dots

Solution steps

lo g_{6} (\frac{36 - 4}{21 6 ^{3}})

Apply log rule:

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

lo g_{6} (\frac{36 - 4}{21 6 ^{3}}) = lo g_{6} (36 - 4) - lo g_{6} (21 6^{3})

= lo g_{6} (36 - 4) - lo g_{6} (21 6^{3})

Apply log rule:

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

lo g_{6} (21 6^{3}) = 3 lo g_{6} (216)

= lo g_{6} (36 - 4) - 3 lo g_{6} (216)

Subtract the numbers:

36 - 4 = 32

= lo g_{6} (32) - 3 lo g_{6} (216)

lo g_{6} (32) = 5 lo g_{6} (2)

3 lo g_{6} (216) = 9

= 5 lo g_{6} (2) - 9

lo g_{8} ((\frac{x ^{3} y}{z})^{2})

- ln (57) + ln (123)

lo g_{e} (3 x + 1) + lo g_{e} (2)

\frac{1}{10} ln (10)

2 ln (53)

What is log_{6}((36-4)/(216^3)) ?
The solution to log_{6}((36-4)/(216^3)) is 5log_{6}(2)-9