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

The solution to 5log_{10}(x)+log_{10}(y)-log_{10}(z) is log_{10}((x^5y)/z)

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simplify 5log_{10}(x)+log_{10}(y)-log_{10}(z)

simplify

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

lo g_{10} (\frac{x ^{5} y}{z})

Solution steps

5 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})

= 5 lo g_{10} (x) + lo g_{10} (\frac{y}{z})

Apply log rule:

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

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

= lo g_{10} (x^{5}) + 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^{5}) + lo g_{10} (\frac{y}{z}) = lo g_{10} (x^{5} \frac{y}{z})

= lo g_{10} (x^{5} \frac{y}{z})

Simplify

x^{5} \frac{y}{z} : \frac{x ^{5} y}{z}

= lo g_{10} (\frac{x ^{5} y}{z})

ln (x) + ln (7)

lo g_{2} (\frac{8 x ^{2}}{y}) - 2 lo g_{2} (2 x^{2} y)

3 lo g_{10} (x) - 4 lo g_{10} (y)

lo g_{2} (\frac{6 x}{y})

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