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Popular >

simplify ln(8x^3(x+2)^5)

Solution

simplify

ln (8 x^{3} (x + 2)^{5})

Solution

3 ln (2) + 3 ln (x) + 5 ln (x + 2)

Solution steps

ln (8 x^{3} (x + 2)^{5})

Apply log rule:

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

ln (8 x^{3} (x + 2)^{5}) = ln (8) + ln (x^{3}) + ln ((x + 2)^{5})

= ln (8) + ln (x^{3}) + ln ((x + 2)^{5})

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= ln (8) + 3 ln (x) + ln ((x + 2)^{5})

Apply log rule:

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

ln ((x + 2)^{5}) = 5 ln (x + 2)

= ln (8) + 3 ln (x) + 5 ln (x + 2)

ln (8) = 3 ln (2)

= 3 ln (2) + 3 ln (x) + 5 ln (x + 2)

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Frequently Asked Questions (FAQ)

What is ln(8x^3(x+2)^5) ?
The solution to ln(8x^3(x+2)^5) is 3ln(2)+3ln(x)+5ln(x+2)