What is 5log_{10}(x)+6log_{10}(y) ?

The solution to 5log_{10}(x)+6log_{10}(y) is log_{10}(x^5y^6)

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simplify 5log_{10}(x)+6log_{10}(y)

simplify

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

lo g_{10} (x^{5} y^{6})

Solution steps

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

Apply log rule:

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

5 lo g_{10} (x) = lo g_{10} (x^{5})

= lo g_{10} (x^{5}) + 6 lo g_{10} (y)

Apply log rule:

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

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

= lo g_{10} (x^{5}) + lo g_{10} (y^{6})

Apply log rule:

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

lo g_{10} (x^{5}) + lo g_{10} (y^{6}) = lo g_{10} (x^{5} y^{6})

= lo g_{10} (x^{5} y^{6})

ln (6) - ln (3) + ln (2 x)

lo g_{3} (\frac{3 a}{b c})

5 ln (x) + \frac{1}{2} ln (y)

lo g_{10} (2^{2}) + lo g_{10} (3^{3})

- lo g_{10} (4.73 \cdot 1 0^{- 9})

What is 5log_{10}(x)+6log_{10}(y) ?
The solution to 5log_{10}(x)+6log_{10}(y) is log_{10}(x^5y^6)