What is 2log_{e}(7)+6log_{e}(pi)-log_{e}(3) ?

The solution to 2log_{e}(7)+6log_{e}(pi)-log_{e}(3) is 2ln(7)+ln((pi^6)/3)

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simplify 2log_{e}(7)+6log_{e}(pi)-log_{e}(3)

simplify

2 lo g_{e} (7) + 6 lo g_{e} (π) - lo g_{e} (3)

2 ln (7) + ln (\frac{π ^{6}}{3})

Decimal Notation

9.66158 \dots

Solution steps

2 lo g_{e} (7) + 6 lo g_{e} (π) - lo g_{e} (3)

Apply log rule:

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

6 lo g_{e} (π) = lo g_{e} (π^{6})

= 2 lo g_{e} (7) + lo g_{e} (π^{6}) - lo g_{e} (3)

Apply log rule:

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

lo g_{e} (π^{6}) - lo g_{e} (3) = lo g_{e} (\frac{π ^{6}}{3})

= 2 lo g_{e} (7) + lo g_{e} (\frac{π ^{6}}{3})

Simplify

lo g_{e} (7) : ln (7)

= 2 ln (7) + lo g_{e} (\frac{π ^{6}}{3})

Apply log rule:

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

= 2 ln (7) + ln (\frac{π ^{6}}{3})

lo g_{9} (\frac{m}{8})

3 lo g_{5} (x) + lo g_{5} (y)

- lo g_{10} (2.6 \cdot 1 0^{- 6})

\frac{1}{4} ln (\frac{11}{7})

3 lo g_{10} (a) - 2 lo g_{10} (k)

What is 2log_{e}(7)+6log_{e}(pi)-log_{e}(3) ?
The solution to 2log_{e}(7)+6log_{e}(pi)-log_{e}(3) is 2ln(7)+ln((pi^6)/3)