What is ln(x^6)-5ln(\sqrt[4]{x^4}) ?

The solution to ln(x^6)-5ln(\sqrt[4]{x^4}) is ln(x)

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simplify ln(x^6)-5ln(\sqrt[4]{x^4})

simplify

ln (x^{6}) - 5 ln (4 x^{4})

ln (x)

Solution steps

ln (x^{6}) - 5 ln (4 x^{4})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{6}}{( 4 x ^{4} ) ^{5}} : x

= ln (x)

lo g_{10} (x y)

20 lo g_{10} (\frac{4.2}{2 2})

f (x) = ln (5) + ln (7) - 3 ln^{2} (x)

2 (1 - 2 ln (1) + 3 - 2 ln (3) + 5 - 2 ln (5) + 7 - 2 ln (7))

\frac{1}{2} ln (50) + \frac{1}{2} ln (1 - \frac{1}{2})

What is ln(x^6)-5ln(\sqrt[4]{x^4}) ?
The solution to ln(x^6)-5ln(\sqrt[4]{x^4}) is ln(x)