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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

- ln (5) + ln (4)

2 ln (x) + 4 ln (y) - 6 ln (z)

- (ln (3 x))^{2} - 10 ln (3 x)

- lo g_{10} (8 \cdot 1 0^{- 5})

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