What is 2log_{e}(8)+9log_{e}(pi)-log_{e}(5) ?

The solution to 2log_{e}(8)+9log_{e}(pi)-log_{e}(5) is 6ln(2)+ln((pi^9)/5)

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simplify 2log_{e}(8)+9log_{e}(pi)-log_{e}(5)

simplify

2 lo g_{e} (8) + 9 lo g_{e} (π) - lo g_{e} (5)

6 ln (2) + ln (\frac{π ^{9}}{5})

Decimal Notation

12.85201 \dots

Solution steps

2 lo g_{e} (8) + 9 lo g_{e} (π) - lo g_{e} (5)

Apply log rule:

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

9 lo g_{e} (π) = lo g_{e} (π^{9})

= 2 lo g_{e} (8) + lo g_{e} (π^{9}) - lo g_{e} (5)

Apply log rule:

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

lo g_{e} (π^{9}) - lo g_{e} (5) = lo g_{e} (\frac{π ^{9}}{5})

= 2 lo g_{e} (8) + lo g_{e} (\frac{π ^{9}}{5})

Simplify

lo g_{e} (8) : ln (8)

= 2 ln (8) + lo g_{e} (\frac{π ^{9}}{5})

Apply log rule:

lo g_{e} (x) = ln (x)

= 2 ln (8) + ln (\frac{π ^{9}}{5})

2 ln (8) = 6 ln (2)

= 6 ln (2) + ln (\frac{π ^{9}}{5})

- lo g_{10} (4.2 \times 1 0^{- 4})

lo g_{10} (3 H) - 2 lo g_{10} (3 S) + 5 lo g_{10} (3 B)

lo g_{3} (5 x y)

2 lo g_{y} (- 3 lo g_{x} (- 2 lo g_{10} (x)))

lo g_{2} (\frac{5 y}{7})

What is 2log_{e}(8)+9log_{e}(pi)-log_{e}(5) ?
The solution to 2log_{e}(8)+9log_{e}(pi)-log_{e}(5) is 6ln(2)+ln((pi^9)/5)