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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

8 lo g_{b} (x) + 4 lo g_{b} (z)

3 ln (6 x) + ln (4 y)

2 ln (5) + 3 ln (2)

2 ln (6) - 2 ln (2)

\frac{3}{2} lo g_{10} (x) + \frac{3}{2} lo g_{10} (y)

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