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})

0.7 ln (\frac{14 m}{14 x + 3 y})

- lo g_{10} (1.9 \cdot 1 0^{- 9})

ln (5.1 \cdot 1 0^{- 4}) + 0.94

3.74 + lo g_{10} (\frac{2.475}{0.025})

ln (2 x^{2} + x^{2}) - ln (x)

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)