What is log_{10}(xe^{(y+z)^2}) ?

The solution to log_{10}(xe^{(y+z)^2}) is log_{10}(x)+(y+z)^2log_{10}(e)

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simplify log_{10}(xe^{(y+z)^2})

simplify

lo g_{10} (x e^{(y + z)^{2}})

lo g_{10} (x) + (y + z)^{2} lo g_{10} (e)

Solution steps

lo g_{10} (x e^{(y + z)^{2}})

Apply log rule:

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

lo g_{10} (x e^{(y + z)^{2}}) = lo g_{10} (x) + lo g_{10} (e^{(y + z)^{2}})

= lo g_{10} (x) + lo g_{10} (e^{(y + z)^{2}})

Apply log rule:

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

lo g_{10} (e^{(y + z)^{2}}) = (y + z)^{2} lo g_{10} (e)

= lo g_{10} (x) + (y + z)^{2} lo g_{10} (e)

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What is log_{10}(xe^{(y+z)^2}) ?
The solution to log_{10}(xe^{(y+z)^2}) is log_{10}(x)+(y+z)^2log_{10}(e)