What is simplify-((1))/((2))ln^4(x^2)-((1))/((2))ln(x^2) ?

The solution to simplify-((1))/((2))ln^4(x^2)-((1))/((2))ln(x^2) is -ln^4(x^2)

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simplify-((1))/((2))ln^4(x^2)-((1))/((2))ln(x^2)

simplify

- \frac{( 1 )}{( 2 )} ln^{4} (x^{2}) - \frac{( 1 )}{( 2 )} ln (x^{2})

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

Solution steps

- \frac{( 1 )}{( 2 )} ln^{4} (x^{2}) - \frac{( 1 )}{( 2 )} ln (x^{2})

Apply log rule:

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

\frac{( 1 )}{( 2 )} ln^{4} (x^{2}) = ln^{4} ((x^{2})^{\frac{( 1 )}{( 2 )}})

= - ln^{4} ((x^{2})^{\frac{( 1 )}{( 2 )}}) - \frac{( 1 )}{( 2 )} ln (x^{2})

Apply log rule:

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

\frac{( 1 )}{( 2 )} ln (x^{2}) = ln ((x^{2})^{\frac{( 1 )}{( 2 )}})

= - ln^{4} ((x^{2})^{\frac{( 1 )}{( 2 )}}) - ln ((x^{2})^{\frac{( 1 )}{( 2 )}})

Rewrite

- ln^{4} ((x^{2})^{\frac{( 1 )}{( 2 )}}) - ln ((x^{2})^{\frac{( 1 )}{( 2 )}})

- (ln^{4} ((x^{2})^{\frac{( 1 )}{( 2 )}}) + ln ((x^{2})^{\frac{( 1 )}{( 2 )}}))

= - (ln^{4} ((x^{2})^{\frac{( 1 )}{( 2 )}}) + ln ((x^{2})^{\frac{( 1 )}{( 2 )}}))

Apply log rule:

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

ln^{4} ((x^{2})^{\frac{( 1 )}{( 2 )}}) + ln ((x^{2})^{\frac{( 1 )}{( 2 )}}) = ln^{4} ((x^{2})^{\frac{1}{2}} (x^{2})^{\frac{1}{2}})

= - ln^{4} ((x^{2})^{\frac{1}{2}} (x^{2})^{\frac{1}{2}})

Simplify

(x^{2})^{\frac{( 1 )}{( 2 )}} (x^{2})^{\frac{( 1 )}{( 2 )}} : x^{2}

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

lo g_{5} ((\frac{x}{2 y})^{8})

\frac{( ln ( 0.25 ) + ln ( 0.5 ) + ln ( 0.75 ) ) \cdot 2 \cdot 0.25}{2}

\frac{ln ( 5.999 ) - ln ( 6 )}{5.999 - 6}

ln (3.5 \cdot 1 0^{- 14})

2 - 0.009 lo g_{10} (\frac{1.3 9 ^{2}}{4.9 3 ^{3}})

What is simplify-((1))/((2))ln^4(x^2)-((1))/((2))ln(x^2) ?
The solution to simplify-((1))/((2))ln^4(x^2)-((1))/((2))ln(x^2) is -ln^4(x^2)