What is 2log_{6}(7)-8log_{6}(10) ?

The solution to 2log_{6}(7)-8log_{6}(10) is log_{6}((49)/(10^8))

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simplify 2log_{6}(7)-8log_{6}(10)

simplify

2 lo g_{6} (7) - 8 lo g_{6} (10)

lo g_{6} (\frac{49}{1 0 ^{8}})

Decimal Notation

- 8.10871 \dots

Solution steps

2 lo g_{6} (7) - 8 lo g_{6} (10)

2 lo g_{6} (7) = lo g_{6} (7^{2})

- 8 lo g_{6} (10) = - lo g_{6} (1 0^{8})

= lo g_{6} (7^{2}) - lo g_{6} (1 0^{8})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{6} (7^{2}) - lo g_{6} (1 0^{8}) = lo g_{6} (\frac{7 ^{2}}{1 0 ^{8}})

= lo g_{6} (\frac{7 ^{2}}{1 0 ^{8}})

7^{2} = 49

= lo g_{6} (\frac{49}{1 0 ^{8}})

lo g_{2} (\frac{ab}{c d})

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

20 ln (\frac{1400}{1400 + 100 ( 20 )}) + 9.8 (20)

- lo g_{10} (1.6 \times 1 0^{- 4})

lo g_{4} (\frac{4}{x})

What is 2log_{6}(7)-8log_{6}(10) ?
The solution to 2log_{6}(7)-8log_{6}(10) is log_{6}((49)/(10^8))