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

The solution to simplify-log_{e}(2)+6log_{e}(6)-log_{e}(5) is ln(23328/5)

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

simplify

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

ln (\frac{23328}{5})

Decimal Notation

8.44797 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{e} (6^{6}) - lo g_{e} (2) = lo g_{e} (\frac{6 ^{6}}{2})

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

\frac{6 ^{6}}{2} = 23328

= lo g_{e} (23328) - lo g_{e} (5)

Apply log rule:

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

lo g_{e} (23328) - lo g_{e} (5) = lo g_{e} (\frac{23328}{5})

= lo g_{e} (\frac{23328}{5})

Apply log rule:

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

= ln (\frac{23328}{5})

lo g_{2} (x + 3) + 5 lo g_{2} (x - 7) - 3 lo g_{2} (x + 6)

ln (\frac{1.12}{0.031})

ln (2) - ln (9)

- 2 ln ∣ 0.5 ∣ - ln ∣ - 0.75 ∣

- ln ∣ 0 - 3 ∣ + 2 ln ∣ 0 - 2 ∣

What is simplify-log_{e}(2)+6log_{e}(6)-log_{e}(5) ?
The solution to simplify-log_{e}(2)+6log_{e}(6)-log_{e}(5) is ln(23328/5)