What is log_{10}(x^ee^x) ?

The solution to log_{10}(x^ee^x) is elog_{10}(x)+xlog_{10}(e)

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simplify log_{10}(x^ee^x)

simplify

lo g_{10} (x^{e} e^{x})

e lo g_{10} (x) + x lo g_{10} (e)

Solution steps

lo g_{10} (x^{e} e^{x})

Apply log rule:

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

lo g_{10} (x^{e} e^{x}) = lo g_{10} (x^{e}) + lo g_{10} (e^{x})

= lo g_{10} (x^{e}) + lo g_{10} (e^{x})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= e lo g_{10} (x) + lo g_{10} (e^{x})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= e lo g_{10} (x) + x lo g_{10} (e)

2 + lo g_{10} (\frac{8}{0.1})

0.935 \cdot ln (\frac{39 + 273}{337 + 273})

- ln (6 - 3) + 2 ln (6 - 2)

lo g_{2} (5) - lo g_{2} (\frac{1}{6})

4 lo g_{5} (a) - \frac{3}{2} lo g_{5} (b)

What is log_{10}(x^ee^x) ?
The solution to log_{10}(x^ee^x) is elog_{10}(x)+xlog_{10}(e)