What is ln(5x-2)4-8ln(sqrt(4-6x)) ?

The solution to ln(5x-2)4-8ln(sqrt(4-6x)) is ln(((5x-2)^4)/((4-6x)^4))

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simplify ln(5x-2)4-8ln(sqrt(4-6x))

simplify

ln (5 x - 2) 4 - 8 ln (4 - 6 x)

ln (\frac{( 5 x - 2 ) ^{4}}{( 4 - 6 x ) ^{4}})

Solution steps

ln (5 x - 2) \cdot 4 - 8 ln (4 - 6 x)

Apply log rule:

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

4 ln (5 x - 2) = ln ((5 x - 2)^{4})

= ln ((5 x - 2)^{4}) - 8 ln (- 6 x + 4)

Apply log rule:

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

8 ln (- 6 x + 4) = ln ((- 6 x + 4)^{8})

= ln ((5 x - 2)^{4}) - ln ((- 6 x + 4)^{8})

Apply log rule:

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

ln ((5 x - 2)^{4}) - ln ((4 - 6 x)^{8}) = ln (\frac{( 5 x - 2 ) ^{4}}{( - 6 x + 4 ) ^{8}})

= ln (\frac{( 5 x - 2 ) ^{4}}{( 4 - 6 x ) ^{8}})

(4 - 6 x)^{8} = (4 - 6 x)^{4}

= ln (\frac{( 5 x - 2 ) ^{4}}{( 4 - 6 x ) ^{4}})

\frac{1}{3} ln (\frac{7}{26})

- lo g_{10} (2.29 \cdot 1 0^{- 6})

- lo g_{10} (8.9 \cdot 1 0^{- 5})

ln (49) - ln (4)

ln (104) - 2 ln (\frac{104}{77})

What is ln(5x-2)4-8ln(sqrt(4-6x)) ?
The solution to ln(5x-2)4-8ln(sqrt(4-6x)) is ln(((5x-2)^4)/((4-6x)^4))