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

The solution to 6log_{10}(x)+log_{10}(y)-log_{10}(z) is log_{10}((x^6y)/z)

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simplify 6log_{10}(x)+log_{10}(y)-log_{10}(z)

simplify

6 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

lo g_{10} (\frac{x ^{6} y}{z})

Solution steps

6 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (y) - lo g_{10} (z) = lo g_{10} (\frac{y}{z})

= 6 lo g_{10} (x) + lo g_{10} (\frac{y}{z})

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

= lo g_{10} (x^{6}) + lo g_{10} (\frac{y}{z})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (x^{6}) + lo g_{10} (\frac{y}{z}) = lo g_{10} (x^{6} \frac{y}{z})

= lo g_{10} (x^{6} \frac{y}{z})

Simplify

x^{6} \frac{y}{z} : \frac{x ^{6} y}{z}

= lo g_{10} (\frac{x ^{6} y}{z})

ln (y) - ln (x)

lo g_{10} (a) - lo g_{10} (b) - lo g_{10} (c)

lo g_{3} (5) + lo g_{3} (2)

lo g_{10} (4) + lo g_{10} (6) - lo g_{10} (2)

lo g_{15} (15 x)

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