What is log_{10}((b^3)/a) ?

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

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simplify log_{10}((b^3)/a)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (b^{3}) : 3 lo g_{10} (b)

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

lo g_{10} (m^{n}) - lo g_{10} (p^{q})

- 3 lo g_{5} (\frac{1}{x}) + \frac{1}{2} lo g_{5} (x)

\frac{1}{2} lo g_{7} (x) - lo g_{7} (x + 1)

\frac{1}{2} ln (x) + \frac{1}{2} ln (x - 1)

ln (2 b \frac{b + 1}{b - 1})

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