What is 2log_{5}(100)-4log_{5}(50) ?

The solution to 2log_{5}(100)-4log_{5}(50) is -4

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simplify 2log_{5}(100)-4log_{5}(50)

simplify

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

- 4

Solution steps

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

2 lo g_{5} (100) = lo g_{5} (10 0^{2})

- 4 lo g_{5} (50) = - lo g_{5} (5 0^{4})

= lo g_{5} (10 0^{2}) - lo g_{5} (5 0^{4})

Apply log rule:

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

lo g_{5} (10 0^{2}) - lo g_{5} (5 0^{4}) = lo g_{5} (\frac{10 0 ^{2}}{5 0 ^{4}})

= lo g_{5} (\frac{10 0 ^{2}}{5 0 ^{4}})

\frac{10 0 ^{2}}{5 0 ^{4}} = 5^{- 4}

= lo g_{5} (5^{- 4})

Apply log rule:

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

= - 4

(- 5 g) (x)

\frac{3}{2} + \frac{3}{5}

\frac{cos ( a )}{1 + cot ^{2} ( a )}

3 x^{2 n} (x^{n + 1} - 4 x^{n} + 5)

\frac{- 42}{6}

What is 2log_{5}(100)-4log_{5}(50) ?
The solution to 2log_{5}(100)-4log_{5}(50) is -4