What is ln(9e)+ln(e^9)+ln(4)e^4 ?

The solution to ln(9e)+ln(e^9)+ln(4)e^4 is 2ln(3)+10+2e^4ln(2)

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simplify ln(9e)+ln(e^9)+ln(4)e^4

simplify

ln (9 e) + ln (e^{9}) + ln (4) e^{4}

2 ln (3) + 10 + 2 e^{4} ln (2)

Decimal Notation

87.88633 \dots

Solution steps

ln (9 e) + ln (e^{9}) + ln (4) e^{4}

Apply log rule:

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

ln (9 e) = ln (9) + ln (e)

= ln (9) + ln (e) + ln (e^{9}) + e^{4} ln (4)

Apply log rule:

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

ln (e^{9}) = 9 ln (e)

= ln (9) + ln (e) + 9 ln (e) + ln (4) e^{4}

Add similar elements:

ln (e) + 9 ln (e) = 10 ln (e)

= ln (9) + 10 ln (e) + e^{4} ln (4)

10 ln (e) = 10

= ln (9) + 10 + e^{4} ln (4)

ln (9) = 2 ln (3)

ln (4) e^{4} = 2 e^{4} ln (2)

= 2 ln (3) + 10 + 2 e^{4} ln (2)

6 [4 ln (x) - ln (x + 5) - ln (x - 5)]

lo g_{3} (\frac{x - 1 ^{4}}{x + 1 ^{9}})

10 ln (\frac{3}{2})

lo g_{3} (81 x^{2})

What is ln(9e)+ln(e^9)+ln(4)e^4 ?
The solution to ln(9e)+ln(e^9)+ln(4)e^4 is 2ln(3)+10+2e^4ln(2)