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

The solution to log_{10}(3)log_{10}(2)+2log_{10}(3) is log_{10}(9*2^{log_{10}(3)})

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

simplify

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

lo g_{10} (9 \cdot 2^{l o g_{10} (3)})

Decimal

1.09787 \dots

Solution steps

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

Apply log rule:

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

lo g_{10} (3) lo g_{10} (2) = lo g_{10} (2^{l o g_{10} (3)})

= lo g_{10} (2^{l o g_{10} (3)}) + 2 lo g_{10} (3)

Apply log rule:

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

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

= lo g_{10} (2^{l o g_{10} (3)}) + lo g_{10} (3^{2})

Apply log rule:

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

lo g_{10} (2^{l o g_{10} (3)}) + lo g_{10} (3^{2}) = lo g_{10} (3^{2} \cdot 2^{l o g_{10} (3)})

= lo g_{10} (3^{2} \cdot 2^{l o g_{10} (3)})

3^{2} = 9

= lo g_{10} (9 \cdot 2^{l o g_{10} (3)})

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9 ln (x + 3) - 5 ln (x)

ln (\frac{x}{x + 1}) + \frac{1}{x + 1} + c

ln (\frac{x + a}{x - a})

2 ln (- 4 ln (x + 2))

What is log_{10}(3)log_{10}(2)+2log_{10}(3) ?
The solution to log_{10}(3)log_{10}(2)+2log_{10}(3) is log_{10}(9*2^{log_{10}(3)})