What is rationalize log_{10}(4)+2log_{10}(x) ?

The solution to rationalize log_{10}(4)+2log_{10}(x) is log_{10}(4x^2)

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rationalize log_{10}(4)+2log_{10}(x)

rationalize

lo g_{10} (4) + 2 lo g_{10} (x)

lo g_{10} (4 x^{2})

Solution steps

lo g_{10} (4) + 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} (4) + lo g_{10} (x^{2})

Apply log rule:

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

lo g_{10} (4) + lo g_{10} (x^{2}) = lo g_{10} (4 x^{2})

= lo g_{10} (4 x^{2})

ln (\frac{x + 2}{e ^{x}})

ln (\frac{1}{9 + 9 e ^{x}} \cdot \frac{1}{8 + 8 e ^{x}})

ln (\frac{0.09175}{0.05722})

What is rationalize log_{10}(4)+2log_{10}(x) ?
The solution to rationalize log_{10}(4)+2log_{10}(x) is log_{10}(4x^2)