What is 5log_{10}(a)-log_{10}(b)+3log_{10}(c) ?

The solution to 5log_{10}(a)-log_{10}(b)+3log_{10}(c) is log_{10}((a^5c^3)/b)

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simplify 5log_{10}(a)-log_{10}(b)+3log_{10}(c)

simplify

5 lo g_{10} (a) - lo g_{10} (b) + 3 lo g_{10} (c)

lo g_{10} (\frac{a ^{5} c ^{3}}{b})

Solution steps

5 lo g_{10} (a) - lo g_{10} (b) + 3 lo g_{10} (c)

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

3 lo g_{10} (c) = lo g_{10} (c^{3})

= lo g_{10} (a^{5}) - lo g_{10} (b) + lo g_{10} (c^{3})

Apply log rule:

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

lo g_{10} (a^{5}) - lo g_{10} (b) = lo g_{10} (\frac{a ^{5}}{b})

= lo g_{10} (\frac{a ^{5}}{b}) + lo g_{10} (c^{3})

Apply log rule:

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

lo g_{10} (\frac{a ^{5}}{b}) + lo g_{10} (c^{3}) = lo g_{10} (\frac{a ^{5}}{b} c^{3})

= lo g_{10} (\frac{a ^{5}}{b} c^{3})

Simplify

\frac{a ^{5}}{b} c^{3} : \frac{a ^{5} c ^{3}}{b}

= lo g_{10} (\frac{a ^{5} c ^{3}}{b})

lo g_{t} (M) + lo g_{t} (N)

- \frac{11}{20} lo g_{2} (\frac{11}{20}) - \frac{9}{20} lo g_{2} (\frac{9}{20})

lo g_{10} (9) + lo g_{10} (20) - lo g_{10} (4)

lo g_{10} (9) + lo g_{10} (20) - lo g_{10} (5)

What is 5log_{10}(a)-log_{10}(b)+3log_{10}(c) ?
The solution to 5log_{10}(a)-log_{10}(b)+3log_{10}(c) is log_{10}((a^5c^3)/b)