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

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

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

simplify

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

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

Solution steps

x - \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}})

= x - 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}})

= x - 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}}})

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

Combine same powers :

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

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

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

lo g_{9} (\frac{x ( x ^{2} + 7 )}{x ^{2} - 7})

9 lo g_{22} (2)

- lo g_{10} (3.2 e^{- 4})

lo g_{e} ((\frac{y - 1}{3})^{2})

16 + 4 ln (\frac{5}{3})

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