What is log_{2}((pi-0.1)/(10^{-6)}) ?

The solution to log_{2}((pi-0.1)/(10^{-6)}) is log_{2}(pi-0.1)--6log_{2}(10)

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simplify log_{2}((pi-0.1)/(10^{-6)})

simplify

lo g_{2} (\frac{π - 0.1}{1 0 ^{- 6}})

lo g_{2} (π - 0.1) - - 6 lo g_{2} (10)

Decimal Notation

- 18.32674 \dots

Solution steps

lo g_{2} (\frac{π - 0.1}{1 0 ^{- 6}})

Apply log rule:

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

lo g_{2} (\frac{π - 0.1}{1 0 ^{- 6}}) = lo g_{2} (π - 0.1) - lo g_{2} (1 0^{- 6})

= lo g_{2} (π - 0.1) - lo g_{2} (1 0^{- 6})

Apply log rule:

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

lo g_{2} (1 0^{- 6}) = - 6 lo g_{2} (10)

= lo g_{2} (π - 0.1) - - 6 lo g_{2} (10)

lo g_{b} (7 x \cdot 2 y)

1 - lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 3)

lo g_{7} (x y)

2 lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (\frac{x ^{5}}{z y})

What is log_{2}((pi-0.1)/(10^{-6)}) ?
The solution to log_{2}((pi-0.1)/(10^{-6)}) is log_{2}(pi-0.1)--6log_{2}(10)