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

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

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

simplify

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

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

Decimal Notation

11.44200 \dots

Solution steps

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

Apply log rule:

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

lo g_{e} (\frac{π ^{9}}{8}) = lo g_{e} (π^{9}) - lo g_{e} (8)

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

Apply log rule:

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

lo g_{e} (π^{9}) = 9 lo g_{e} (π)

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

- lo g_{10} (6.86 \cdot 1 0^{- 8})

2 x + ln (cos (3 x)) - \frac{1}{2} ln (x - 4)

- \frac{ln ( \frac{5}{22} )}{2 ln ( \frac{110}{7} )}

ln (100 e^{x})

- ln (\frac{1}{0.99})

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