What is 4log_{5}(100)-8log_{5}(50) ?

The solution to 4log_{5}(100)-8log_{5}(50) is -8

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simplify 4log_{5}(100)-8log_{5}(50)

simplify

4 lo g_{5} (100) - 8 lo g_{5} (50)

- 8

Solution steps

4 lo g_{5} (100) - 8 lo g_{5} (50)

4 lo g_{5} (100) = lo g_{5} (10 0^{4})

- 8 lo g_{5} (50) = - lo g_{5} (5 0^{8})

= lo g_{5} (10 0^{4}) - lo g_{5} (5 0^{8})

Apply log rule:

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

lo g_{5} (10 0^{4}) - lo g_{5} (5 0^{8}) = lo g_{5} (\frac{10 0 ^{4}}{5 0 ^{8}})

= lo g_{5} (\frac{10 0 ^{4}}{5 0 ^{8}})

\frac{10 0 ^{4}}{5 0 ^{8}} = 5^{- 8}

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

Apply log rule:

lo g_{a} (a^{b}) = b

= - 8

x^{4} - 3 x^{3} - 11 x^{2} + 3 x + 10

e^{2 (l n (x))}

- 2 - 32

2 x^{3} + 3 x - 5

What is 4log_{5}(100)-8log_{5}(50) ?
The solution to 4log_{5}(100)-8log_{5}(50) is -8