What is 5log_{10}(xy)+log_{10}(z) ?

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

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simplify 5log_{10}(xy)+log_{10}(z)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

(x y)^{5} z : x^{5} y^{5} z

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

3 lo g_{2} (x) - lo g_{2} (2) - lo g_{2} (x + 2)

lo g_{5} (2) - 2 lo g_{5} (y)

lo g_{2} (\frac{x}{a ^{2}})

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