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

The solution to 3log_{10}(x)+log_{10}(7)-2log_{10}(y) is log_{10}((x^3*7)/(y^2))

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

simplify

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

lo g_{10} (\frac{x ^{3} \cdot 7}{y ^{2}})

Solution steps

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

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}) + lo g_{10} (7) - 2 lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x^{3}) + lo g_{10} (7) = lo g_{10} (7 x^{3})

= lo g_{10} (x^{3} \cdot 7) - 2 lo g_{10} (y)

Apply log rule:

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

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

= lo g_{10} (7 x^{3}) - lo g_{10} (y^{2})

Apply log rule:

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

lo g_{10} (7 x^{3}) - lo g_{10} (y^{2}) = lo g_{10} (\frac{7 x ^{3}}{y ^{2}})

= lo g_{10} (\frac{x ^{3} \cdot 7}{y ^{2}})

- \frac{2 ln ( 2 )}{ln ( 3 )}

ln (x + 5) - ln (x)

lo g_{4}^{2} (x) + lo g_{4} (x)

ln (9) - ln (7)

lo g_{10} (5 \cdot 1 0^{- 5})

What is 3log_{10}(x)+log_{10}(7)-2log_{10}(y) ?
The solution to 3log_{10}(x)+log_{10}(7)-2log_{10}(y) is log_{10}((x^3*7)/(y^2))