What is 5log_{5}(7y+1)+1/2 log_{5}(y+5) ?

The solution to 5log_{5}(7y+1)+1/2 log_{5}(y+5) is log_{5}((7y+1)^5(y+5)^{1/2})

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simplify 5log_{5}(7y+1)+1/2 log_{5}(y+5)

simplify

5 lo g_{5} (7 y + 1) + \frac{1}{2} lo g_{5} (y + 5)

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

Solution steps

5 lo g_{5} (7 y + 1) + \frac{1}{2} lo g_{5} (y + 5)

Apply log rule:

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

5 lo g_{5} (7 y + 1) = lo g_{5} ((7 y + 1)^{5})

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

ln (\frac{2 x}{a ^{2}})

6 lo g_{5} (z - 4) - 3 lo g_{5} (z + 5)

lo g_{10} (\frac{10}{x ( x ^{2} + 1 ) ( x ^{4} + 2 )})

\frac{2}{7} ln ∣ x + 6 ∣ + \frac{5}{7} ln ∣ x - 1 ∣

- lo g_{10} (0.6 (1 0^{- 3}))

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