What is 2log_{e}(6)+2log_{e}(pi)-log_{e}(5) ?

The solution to 2log_{e}(6)+2log_{e}(pi)-log_{e}(5) is ln((36pi^2)/5)

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simplify 2log_{e}(6)+2log_{e}(pi)-log_{e}(5)

simplify

2 lo g_{e} (6) + 2 lo g_{e} (π) - lo g_{e} (5)

ln (\frac{36 π ^{2}}{5})

Decimal Notation

4.26354 \dots

Solution steps

2 lo g_{e} (6) + 2 lo g_{e} (π) - lo g_{e} (5)

Apply log rule:

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

2 lo g_{e} (6) = lo g_{e} (6^{2})

= lo g_{e} (6^{2}) + 2 lo g_{e} (π) - lo g_{e} (5)

Apply log rule:

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

2 lo g_{e} (π) = lo g_{e} (π^{2})

= lo g_{e} (6^{2}) + lo g_{e} (π^{2}) - lo g_{e} (5)

Apply log rule:

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

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

= lo g_{e} (6^{2} π^{2}) - lo g_{e} (5)

6^{2} = 36

= lo g_{e} (36 π^{2}) - lo g_{e} (5)

Apply log rule:

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

lo g_{e} (36 π^{2}) - lo g_{e} (5) = lo g_{e} (\frac{36 π ^{2}}{5})

= lo g_{e} (\frac{36 π ^{2}}{5})

Apply log rule:

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

= ln (\frac{36 π ^{2}}{5})

3 ln (x) - 2 ln (x + 1)

lo g_{10} (\frac{z}{y})

ln (\frac{x}{y}) - \frac{1}{2} ln (1 + \frac{x ^{2}}{y ^{2}})

- \frac{1}{0.07} ln (\frac{1}{7})

- lo g_{10} (2.99 \cdot 1 0^{- 3})

What is 2log_{e}(6)+2log_{e}(pi)-log_{e}(5) ?
The solution to 2log_{e}(6)+2log_{e}(pi)-log_{e}(5) is ln((36pi^2)/5)