What is 4log_{10}(x)-log_{10}(1/x)-log_{10}(y) ?

The solution to 4log_{10}(x)-log_{10}(1/x)-log_{10}(y) is 5log_{10}(x)-log_{10}(y)

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simplify 4log_{10}(x)-log_{10}(1/x)-log_{10}(y)

simplify

4 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

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

Solution steps

4 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

Simplify

lo g_{10} (\frac{1}{x}) : - lo g_{10} (x)

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

Apply rule:

a - (- b) = a + b

4 lo g_{10} (x) - (- lo g_{10} (x)) = 4 lo g_{10} (x) + lo g_{10} (x)

= 4 lo g_{10} (x) + lo g_{10} (x) - lo g_{10} (y)

Add similar elements:

4 lo g_{10} (x) + lo g_{10} (x) = 5 lo g_{10} (x)

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

lo g_{7} ((5) (c))

3 \cdot ln (pq) + 4 \cdot ln (p q^{2})

\frac{2}{6} lo g_{2} (\frac{2}{6}) + \frac{4}{6} lo g_{2} (\frac{4}{6})

lo g_{4} (2) + 2 lo g_{4} (9)

\frac{1}{5} [lo g_{4} (x) + lo g_{4} (3)] - [lo g_{4} (y)]

What is 4log_{10}(x)-log_{10}(1/x)-log_{10}(y) ?
The solution to 4log_{10}(x)-log_{10}(1/x)-log_{10}(y) is 5log_{10}(x)-log_{10}(y)