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Popular >

simplify 2log_{5}(3)-log_{5}(45)

Solution

simplify

2 lo g_{5} (3) - lo g_{5} (45)

Solution

- 1

Solution steps

2 lo g_{5} (3) - lo g_{5} (45)

Apply log rule:

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

2 lo g_{5} (3) = lo g_{5} (3^{2})

= lo g_{5} (3^{2}) - lo g_{5} (45)

Apply log rule:

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

lo g_{5} (3^{2}) - lo g_{5} (45) = lo g_{5} (\frac{3 ^{2}}{45})

= lo g_{5} (\frac{3 ^{2}}{45})

\frac{3 ^{2}}{45} = 5^{- 1}

= lo g_{5} (5^{- 1})

Apply log rule:

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

= - 1

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Frequently Asked Questions (FAQ)

What is 2log_{5}(3)-log_{5}(45) ?
The solution to 2log_{5}(3)-log_{5}(45) is -1