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Popular >

simplify ln(225)-2ln(3)+ln(e^9)

Solution

simplify

ln (225) - 2 ln (3) + ln (e^{9})

Solution

2 ln (5) + 9

+1

Decimal Notation

12.21887 \dots

Solution steps

ln (225) - 2 ln (3) + ln (e^{9})

Apply log rule:

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

2 ln (3) = ln (3^{2})

= ln (225) - ln (3^{2}) + ln (e^{9})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (225) - ln (3^{2}) = ln (\frac{225}{3 ^{2}})

= ln (\frac{225}{3 ^{2}}) + ln (e^{9})

\frac{225}{3 ^{2}} = 25

= ln (25) + ln (e^{9})

ln (e^{9}) = 9

= ln (25) + 9

ln (25) = 2 ln (5)

= 2 ln (5) + 9

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Frequently Asked Questions (FAQ)

What is ln(225)-2ln(3)+ln(e^9) ?
The solution to ln(225)-2ln(3)+ln(e^9) is 2ln(5)+9