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Popular >

simplify ln((x+1)^53x)

Solution

simplify

ln ((x + 1)^{5} 3 x)

Solution

5 ln (x + 1) + ln (3) + ln (x)

Solution steps

ln ((x + 1)^{5} \cdot 3 x)

Apply log rule:

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

ln ((x + 1)^{5} \cdot 3 x) = ln ((x + 1)^{5}) + ln (3) + ln (x)

= ln ((x + 1)^{5}) + ln (3) + ln (x)

Apply log rule:

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

ln ((x + 1)^{5}) = 5 ln (x + 1)

= 5 ln (x + 1) + ln (3) + ln (x)

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Frequently Asked Questions (FAQ)

What is ln((x+1)^53x) ?
The solution to ln((x+1)^53x) is 5ln(x+1)+ln(3)+ln(x)