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Popular >

simplify 5ln(θ)+5ln(1-θ)

Solution

simplify

5 ln (θ) + 5 ln (1 - θ)

Solution

ln (θ^{5} (1 - θ)^{5})

Solution steps

5 ln (θ) + 5 ln (1 - θ)

Apply log rule:

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

5 ln (θ) = ln (θ^{5})

= ln (θ^{5}) + 5 ln (- θ + 1)

Apply log rule:

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

5 ln (- θ + 1) = ln ((- θ + 1)^{5})

= ln (θ^{5}) + ln ((- θ + 1)^{5})

Apply log rule:

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

ln (θ^{5}) + ln ((1 - θ)^{5}) = ln (θ^{5} (- θ + 1)^{5})

= ln (θ^{5} (1 - θ)^{5})

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Frequently Asked Questions (FAQ)

What is 5ln(θ)+5ln(1-θ) ?
The solution to 5ln(θ)+5ln(1-θ) is ln(θ^5(1-θ)^5)