What is 5*log_{10}(x)+7*log_{10}(y) ?

The solution to 5*log_{10}(x)+7*log_{10}(y) is log_{10}(x^5y^7)

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simplify 5log_{10}(x)+7log_{10}(y)

simplify

5 \cdot lo g_{10} (x) + 7 \cdot lo g_{10} (y)

lo g_{10} (x^{5} y^{7})

Solution steps

5 lo g_{10} (x) + 7 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}) + 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^{5}) + lo g_{10} (y^{7})

Apply log rule:

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

lo g_{10} (x^{5}) + lo g_{10} (y^{7}) = lo g_{10} (x^{5} y^{7})

= lo g_{10} (x^{5} y^{7})

3 ln (x) + \frac{1}{x} + ln (x + 1) + c

lo g_{10} (\frac{( 4 \cdot 1 0 ^{- 7} )}{( 1 0 ^{- 12} )})

ln (\frac{41}{140})

2 lo g_{10} (6) - 0.5 lo g_{10} (9)

lo g_{10} (60 e^{0.032 \cdot 5})

What is 5*log_{10}(x)+7*log_{10}(y) ?
The solution to 5*log_{10}(x)+7*log_{10}(y) is log_{10}(x^5y^7)