What is (log_{e}(a))/2-log_{e}(b)-3log_{e}(c) ?

The solution to (log_{e}(a))/2-log_{e}(b)-3log_{e}(c) is (ln(a))/2-ln(bc^3)

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simplify (log_{e}(a))/2-log_{e}(b)-3log_{e}(c)

simplify

\frac{lo g _{e} ( a )}{2} - lo g_{e} (b) - 3 lo g_{e} (c)

\frac{ln ( a )}{2} - ln (b c^{3})

Solution steps

\frac{lo g _{e} ( a )}{2} - lo g_{e} (b) - 3 lo g_{e} (c)

Apply log rule:

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

3 lo g_{e} (c) = lo g_{e} (c^{3})

= \frac{lo g _{e} ( a )}{2} - lo g_{e} (b) - lo g_{e} (c^{3})

Rewrite

- lo g_{e} (b) - lo g_{e} (c^{3})

- (lo g_{e} (b) + lo g_{e} (c^{3}))

= \frac{lo g _{e} ( a )}{2} - (lo g_{e} (b) + lo g_{e} (c^{3}))

Apply log rule:

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

lo g_{e} (b) + lo g_{e} (c^{3}) = lo g_{e} (b c^{3})

= \frac{lo g _{e} ( a )}{2} - lo g_{e} (b c^{3})

Simplify

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

= \frac{ln ( a )}{2} - lo g_{e} (b c^{3})

Apply log rule:

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

= \frac{ln ( a )}{2} - ln (b c^{3})

lo g_{10} (0.37 x)

ln (\frac{82.14}{500})

- lo g_{10} (5.5 \cdot 1 0^{- 3} \cdot 2)

6 lo g_{3} (y) - \frac{1}{4} lo g_{3} (z) + 5 lo g_{3} (x)

\frac{1}{2} ln ∣ y - 1 ∣ - \frac{1}{2} ln ∣ y + 1 ∣

What is (log_{e}(a))/2-log_{e}(b)-3log_{e}(c) ?
The solution to (log_{e}(a))/2-log_{e}(b)-3log_{e}(c) is (ln(a))/2-ln(bc^3)