What is 3log_{5}(2x)-4log_{5}(x-1) ?

The solution to 3log_{5}(2x)-4log_{5}(x-1) is log_{5}((8x^3)/((x-1)^4))

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simplify 3log_{5}(2x)-4log_{5}(x-1)

simplify

3 lo g_{5} (2 x) - 4 lo g_{5} (x - 1)

lo g_{5} (\frac{8 x ^{3}}{( x - 1 ) ^{4}})

Solution steps

3 lo g_{5} (2 x) - 4 lo g_{5} (x - 1)

Apply log rule:

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

3 lo g_{5} (2 x) = lo g_{5} ((2 x)^{3})

= lo g_{5} ((2 x)^{3}) - 4 lo g_{5} (x - 1)

Apply log rule:

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

4 lo g_{5} (x - 1) = lo g_{5} ((x - 1)^{4})

= lo g_{5} ((2 x)^{3}) - lo g_{5} ((x - 1)^{4})

Apply log rule:

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

lo g_{5} ((2 x)^{3}) - lo g_{5} ((x - 1)^{4}) = lo g_{5} (\frac{( 2 x ) ^{3}}{( x - 1 ) ^{4}})

= lo g_{5} (\frac{( 2 x ) ^{3}}{( x - 1 ) ^{4}})

Simplify

\frac{( 2 x ) ^{3}}{( x - 1 ) ^{4}} : \frac{8 x ^{3}}{( x - 1 ) ^{4}}

= lo g_{5} (\frac{8 x ^{3}}{( x - 1 ) ^{4}})

- ln (cos (x)) + ln (c)

ln (\frac{112}{100}) + (\frac{1}{2} \cdot 0. 2^{2} - 0.05) \cdot 0.5

- lo g_{10} (4.2 \cdot 1 0^{- 4})

ln (70) - ln (x)

ln (50) - 2 ln (5)

What is 3log_{5}(2x)-4log_{5}(x-1) ?
The solution to 3log_{5}(2x)-4log_{5}(x-1) is log_{5}((8x^3)/((x-1)^4))