What is 6log_{10}(x)+7log_{10}(y) ?

The solution to 6log_{10}(x)+7log_{10}(y) is log_{10}(x^6y^7)

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simplify 6log_{10}(x)+7log_{10}(y)

simplify

6 lo g_{10} (x) + 7 lo g_{10} (y)

lo g_{10} (x^{6} y^{7})

Solution steps

6 lo g_{10} (x) + 7 lo g_{10} (y)

Apply log rule:

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

6 lo g_{10} (x) = lo g_{10} (x^{6})

= lo g_{10} (x^{6}) + 7 lo g_{10} (y)

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} (x^{6}) + lo g_{10} (y^{7})

Apply log rule:

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

lo g_{10} (x^{6}) + lo g_{10} (y^{7}) = lo g_{10} (x^{6} y^{7})

= lo g_{10} (x^{6} y^{7})

ln (\frac{x ^{2} + y ^{2}}{x + y}) - ln (x + y)

- lo g_{10} (1.5 \cdot 1 0^{- 3})

- ln \frac{x}{2} + 1 + ln \frac{x}{2} - 1

- lo g_{10} (4.7 \cdot 1 0^{- 5})

lo g_{10} (2 \cdot 1 0^{- 5})

What is 6log_{10}(x)+7log_{10}(y) ?
The solution to 6log_{10}(x)+7log_{10}(y) is log_{10}(x^6y^7)