What is 1/2 log_{5}(15)-log_{5}(sqrt(75)) ?

The solution to 1/2 log_{5}(15)-log_{5}(sqrt(75)) is -1/2

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simplify 1/2 log_{5}(15)-log_{5}(sqrt(75))

simplify

\frac{1}{2} lo g_{5} (15) - lo g_{5} (75)

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

\frac{1}{2} lo g_{5} (15) - lo g_{5} (75)

Apply log rule:

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

\frac{1}{2} lo g_{5} (15) = lo g_{5} (1 5^{\frac{1}{2}})

= lo g_{5} (1 5^{\frac{1}{2}}) - lo g_{5} (75)

Apply log rule:

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

lo g_{5} (1 5^{\frac{1}{2}}) - lo g_{5} (75) = lo g_{5} (\frac{1 5 ^{\frac{1}{2}}}{75})

= lo g_{5} (\frac{1 5 ^{\frac{1}{2}}}{75})

Cancel

\frac{1 5 ^{\frac{1}{2}}}{75} : \frac{1}{5}

= lo g_{5} (\frac{1}{5})

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

= lo g_{5} (5^{- \frac{1}{2}})

Apply log rule:

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

= - \frac{1}{2}

7 \cdot \frac{1}{5}

2 x + 3 (1 - 2 x) < x + 8

212.9 \cdot (\frac{39.3701}{1}) \cdot (\frac{60}{1})

x - 1 \geq 5

- x^{2} + 25

What is 1/2 log_{5}(15)-log_{5}(sqrt(75)) ?
The solution to 1/2 log_{5}(15)-log_{5}(sqrt(75)) is -1/2