What is 1/2 log_{5}(7)-2log_{5}(x) ?

The solution to 1/2 log_{5}(7)-2log_{5}(x) is log_{5}((7^{1/2})/(x^2))

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simplify 1/2 log_{5}(7)-2log_{5}(x)

simplify

\frac{1}{2} lo g_{5} (7) - 2 lo g_{5} (x)

lo g_{5} (\frac{7 ^{\frac{1}{2}}}{x ^{2}})

Solution steps

\frac{1}{2} lo g_{5} (7) - 2 lo g_{5} (x)

Apply log rule:

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

\frac{1}{2} lo g_{5} (7) = lo g_{5} (7^{\frac{1}{2}})

= lo g_{5} (7^{\frac{1}{2}}) - 2 lo g_{5} (x)

Apply log rule:

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

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

= lo g_{5} (7^{\frac{1}{2}}) - lo g_{5} (x^{2})

Apply log rule:

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

lo g_{5} (7^{\frac{1}{2}}) - lo g_{5} (x^{2}) = lo g_{5} (\frac{7 ^{\frac{1}{2}}}{x ^{2}})

= lo g_{5} (\frac{7 ^{\frac{1}{2}}}{x ^{2}})

lo g_{10} (5) + lo g_{10} (6) - lo g_{10} (2)

4 ln (x + \frac{6}{4}) + ln (x + 1)

ln (10 x) - ln (z)

lo g_{9} ((x y^{3})^{3})

What is 1/2 log_{5}(7)-2log_{5}(x) ?
The solution to 1/2 log_{5}(7)-2log_{5}(x) is log_{5}((7^{1/2})/(x^2))