What is log_{10}((27a)/b) ?

The solution to log_{10}((27a)/b) is 3log_{10}(3)+log_{10}(a)-log_{10}(b)

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simplify log_{10}((27a)/b)

simplify

lo g_{10} (\frac{27 a}{b})

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

Solution steps

lo g_{10} (\frac{27 a}{b})

Apply log rule:

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

lo g_{10} (\frac{27 a}{b}) = lo g_{10} (27 a) - lo g_{10} (b)

= lo g_{10} (27 a) - lo g_{10} (b)

Simplify

lo g_{10} (27 a) : 3 lo g_{10} (3) + lo g_{10} (a)

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

ln (\frac{x}{x - 4}) + ln (\frac{x + 4}{x}) - ln (x^{2} - 16)

3 lo g_{10} (x) + lo g_{10} (2)

ln (4 x^{2})

- lo g_{10} (x + 6) + lo g_{10} (x - 5)

lo g_{10} (\frac{2 x}{5})

What is log_{10}((27a)/b) ?
The solution to log_{10}((27a)/b) is 3log_{10}(3)+log_{10}(a)-log_{10}(b)