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

The solution to log_{e}(8)+9log_{e}(pi)-log_{e}(5) is 3ln(2)+ln((pi^9)/5)

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

simplify

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

3 ln (2) + ln (\frac{π ^{9}}{5})

Decimal Notation

10.77257 \dots

Solution steps

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})

= 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})

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

Apply log rule:

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

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

Apply log rule:

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

= ln (8) + ln (\frac{π ^{9}}{5})

ln (8) = 3 ln (2)

= 3 ln (2) + ln (\frac{π ^{9}}{5})

- ln (\frac{25}{16})

lo g_{9} (u \cdot v \cdot w)

ln (3) \frac{1}{2}

- \frac{6 ln ( 60 )}{ln ( 2 )}

lo g_{5} (28) x^{2} - lo g_{5} (2 x)

What is log_{e}(8)+9log_{e}(pi)-log_{e}(5) ?
The solution to log_{e}(8)+9log_{e}(pi)-log_{e}(5) is 3ln(2)+ln((pi^9)/5)