What is 3log_{10}(x)+2log_{10}(y-4) ?

The solution to 3log_{10}(x)+2log_{10}(y-4) is log_{10}(x^3(y-4)^2)

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simplify 3log_{10}(x)+2log_{10}(y-4)

simplify

3 lo g_{10} (x) + 2 lo g_{10} (y - 4)

lo g_{10} (x^{3} (y - 4)^{2})

Solution steps

3 lo g_{10} (x) + 2 lo g_{10} (y - 4)

Apply log rule:

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

3 lo g_{10} (x) = lo g_{10} (x^{3})

= lo g_{10} (x^{3}) + 2 lo g_{10} (y - 4)

Apply log rule:

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

2 lo g_{10} (y - 4) = lo g_{10} ((y - 4)^{2})

= lo g_{10} (x^{3}) + lo g_{10} ((y - 4)^{2})

Apply log rule:

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

lo g_{10} (x^{3}) + lo g_{10} ((y - 4)^{2}) = lo g_{10} (x^{3} (y - 4)^{2})

= lo g_{10} (x^{3} (y - 4)^{2})

- \frac{5 ln ( 20 )}{ln ( 2 )}

ln (x^{5}) - 2 ln (x^{3})

ln (\frac{4 ( 1 - x )}{y ^{3}})

lo g_{10} (2 \cdot 1 0^{- 3})

ln (77) - ln (0.1)

What is 3log_{10}(x)+2log_{10}(y-4) ?
The solution to 3log_{10}(x)+2log_{10}(y-4) is log_{10}(x^3(y-4)^2)