What is 7log_{10}(y)+2log_{10}(5y+3) ?

The solution to 7log_{10}(y)+2log_{10}(5y+3) is log_{10}(y^7(5y+3)^2)

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simplify 7log_{10}(y)+2log_{10}(5y+3)

simplify

7 lo g_{10} (y) + 2 lo g_{10} (5 y + 3)

lo g_{10} (y^{7} (5 y + 3)^{2})

Solution steps

7 lo g_{10} (y) + 2 lo g_{10} (5 y + 3)

Apply log rule:

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

7 lo g_{10} (y) = lo g_{10} (y^{7})

= lo g_{10} (y^{7}) + 2 lo g_{10} (5 y + 3)

Apply log rule:

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

2 lo g_{10} (5 y + 3) = lo g_{10} ((5 y + 3)^{2})

= lo g_{10} (y^{7}) + lo g_{10} ((5 y + 3)^{2})

Apply log rule:

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

lo g_{10} (y^{7}) + lo g_{10} ((5 y + 3)^{2}) = lo g_{10} (y^{7} (5 y + 3)^{2})

= lo g_{10} (y^{7} (5 y + 3)^{2})

ln 2 - \frac{1}{2} - ln \frac{1}{6} + \frac{1}{24}

lo g_{7} (\frac{6 x}{y ^{2}})

f (y) = \frac{1}{2} lo g_{10} (- 2 lo g_{10} (y))

lo g_{7} (49 x^{2})

\frac{48}{343 ln ( 7 )} + \frac{1}{e} - \frac{1}{e ^{3}}

What is 7log_{10}(y)+2log_{10}(5y+3) ?
The solution to 7log_{10}(y)+2log_{10}(5y+3) is log_{10}(y^7(5y+3)^2)