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Popular >

simplify log_{e}((1+θ)x^θ)

Solution

simplify

lo g_{e} ((1 + θ) x^{θ})

Solution

ln (1 + θ) + θ ln (x)

Solution steps

lo g_{e} ((1 + θ) x^{θ})

Apply log rule:

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

lo g_{e} ((1 + θ) x^{θ}) = lo g_{e} (1 + θ) + lo g_{e} (x^{θ})

= lo g_{e} (θ + 1) + lo g_{e} (x^{θ})

Apply log rule:

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

lo g_{e} (x^{θ}) = θ lo g_{e} (x)

= lo g_{e} (1 + θ) + θ lo g_{e} (x)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (θ + 1) + θ lo g_{e} (x)

Simplify

lo g_{e} (x) : ln (x)

= ln (θ + 1) + θ ln (x)

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Frequently Asked Questions (FAQ)

What is log_{e}((1+θ)x^θ) ?
The solution to log_{e}((1+θ)x^θ) is ln(1+θ)+θln(x)