What is log_{10}(x-3)+2log_{10}(x) ?

The solution to log_{10}(x-3)+2log_{10}(x) is log_{10}((x-3)x^2)

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simplify log_{10}(x-3)+2log_{10}(x)

simplify

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

lo g_{10} ((x - 3) x^{2})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{10} (x) = lo g_{10} (x^{2})

= lo g_{10} (x - 3) + lo g_{10} (x^{2})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (x - 3) + lo g_{10} (x^{2}) = lo g_{10} (x^{2} (x - 3))

= lo g_{10} ((x - 3) x^{2})

lo g_{7} (2 \cdot 6) + lo g_{7} (3)

- \frac{1}{14} ln ∣ 3 x - 1 ∣ - 3 ln ∣ 3 - 2 ∣ + \frac{32}{7} ln ∣ 3 + 3 ∣

lo g_{b} (z^{6} x)

\frac{2 ln ( 3 )}{ln ( 7 )} + 6

What is log_{10}(x-3)+2log_{10}(x) ?
The solution to log_{10}(x-3)+2log_{10}(x) is log_{10}((x-3)x^2)