What is simplify-1/2 log_{15}(17)+1/2 log_{15}(3) ?

The solution to simplify-1/2 log_{15}(17)+1/2 log_{15}(3) is 1/2 log_{15}(3/17)

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simplify-1/2 log_{15}(17)+1/2 log_{15}(3)

simplify

- \frac{1}{2} lo g_{15} (17) + \frac{1}{2} lo g_{15} (3)

\frac{1}{2} lo g_{15} (\frac{3}{17})

Decimal Notation

- 0.32026 \dots

Solution steps

- \frac{1}{2} lo g_{15} (17) + \frac{1}{2} lo g_{15} (3)

Apply log rule:

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

\frac{1}{2} lo g_{15} (17) = lo g_{15} (1 7^{\frac{1}{2}})

= - lo g_{15} (1 7^{\frac{1}{2}}) + \frac{1}{2} lo g_{15} (3)

Apply log rule:

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

\frac{1}{2} lo g_{15} (3) = lo g_{15} (3^{\frac{1}{2}})

= - lo g_{15} (1 7^{\frac{1}{2}}) + lo g_{15} (3^{\frac{1}{2}})

Apply log rule:

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

lo g_{15} (3^{\frac{1}{2}}) - lo g_{15} (1 7^{\frac{1}{2}}) = lo g_{15} (\frac{3 ^{\frac{1}{2}}}{1 7 ^{\frac{1}{2}}})

= lo g_{15} (\frac{3 ^{\frac{1}{2}}}{1 7 ^{\frac{1}{2}}})

Combine same powers :

= lo g_{15} (\frac{3}{17})

Rewrite as

= lo g_{15} ((\frac{3}{17})^{\frac{1}{2}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} lo g_{15} (\frac{3}{17})

e^{(3^{2} - 1)} 3^{3} + ln (5 \cdot 3^{3}) 3^{2} + 15

\frac{1}{5} ln (\frac{0.267 - 0.017}{0.095 - 0.017})

ln (l e^{- l x})

(\frac{1}{2} + 1 + ln (- 2) + 2 ln (3) + 2) - (ln (- 3) + 2 ln (2))

ln (\frac{5}{610.0 4 ^{2}})

What is simplify-1/2 log_{15}(17)+1/2 log_{15}(3) ?
The solution to simplify-1/2 log_{15}(17)+1/2 log_{15}(3) is 1/2 log_{15}(3/17)