What is ln(e^5*3^{2log_{3}(3)}) ?

The solution to ln(e^5*3^{2log_{3}(3)}) is 5+2ln(3)

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simplify ln(e^5*3^{2log_{3}(3)})

simplify

ln (e^{5} \cdot 3^{2 l o g_{3} (3)})

5 + 2 ln (3)

Decimal Notation

7.19722 \dots

Solution steps

ln (e^{5} \cdot 3^{2 l o g_{3} (3)})

Apply log rule:

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

ln (e^{5} \cdot 3^{2 l o g_{3} (3)}) = ln (e^{5}) + ln (3^{2 l o g_{3} (3)})

= ln (e^{5}) + ln (3^{2 l o g_{3} (3)})

Apply log rule:

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

ln (e^{5}) = 5 ln (e)

= 5 ln (e) + ln (3^{2 l o g_{3} (3)})

Apply log rule:

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

ln (3^{2 l o g_{3} (3)}) = 2 lo g_{3} (3) ln (3)

= 5 ln (e) + 2 lo g_{3} (3) ln (3)

5 ln (e) = 5

2 lo g_{3} (3) ln (3) = 2 ln (3)

= 5 + 2 ln (3)

ln (\frac{m ! e ^{- x}}{( 1 + x ) ^{m + 1}})

ln (x \cdot x)

lo g_{10} (\frac{[ 0.5 ]}{[ 0.4 ]}) + 3.77

ln (\frac{2 x + 1}{x + 2})

lo g_{e} (\frac{y}{2})

What is ln(e^5*3^{2log_{3}(3)}) ?
The solution to ln(e^5*3^{2log_{3}(3)}) is 5+2ln(3)