What is simplify-3(1/2 ln(2^2-9)-1/2 ln((-2)^2-9)) ?

The solution to simplify-3(1/2 ln(2^2-9)-1/2 ln((-2)^2-9)) is 0

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simplify-3(1/2 ln(2^2-9)-1/2 ln((-2)^2-9))

simplify

- 3 (\frac{1}{2} ln (2^{2} - 9) - \frac{1}{2} ln ((- 2)^{2} - 9))

0

Solution steps

- 3 (\frac{1}{2} ln (2^{2} - 9) - \frac{1}{2} ln ((- 2)^{2} - 9))

Apply log rule:

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

\frac{1}{2} ln (2^{2} - 9) = ln ((2^{2} - 9)^{\frac{1}{2}})

= - 3 (ln ((2^{2} - 9)^{\frac{1}{2}}) - \frac{1}{2} ln ((- 2)^{2} - 9))

Apply log rule:

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

\frac{1}{2} ln ((- 2)^{2} - 9) = ln (((- 2)^{2} - 9)^{\frac{1}{2}})

= - 3 (ln ((2^{2} - 9)^{\frac{1}{2}}) - ln (((- 2)^{2} - 9)^{\frac{1}{2}}))

Apply log rule:

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

ln ((2^{2} - 9)^{\frac{1}{2}}) - ln (((- 2)^{2} - 9)^{\frac{1}{2}}) = ln \frac{( 2 ^{2} - 9 ) ^{\frac{1}{2}}}{( ( - 2 ) ^{2} - 9 ) ^{\frac{1}{2}}}

= - 3 ln \frac{( 2 ^{2} - 9 ) ^{\frac{1}{2}}}{( ( - 2 ) ^{2} - 9 ) ^{\frac{1}{2}}}

\frac{( 2 ^{2} - 9 ) ^{\frac{1}{2}}}{( ( - 2 ) ^{2} - 9 ) ^{\frac{1}{2}}} = 1

= - 3 ln (1)

Simplify

ln (1) : 0

= - 3 \cdot 0

Apply rule

0 \cdot a = 0

= 0

- lo g_{10} (2.5 \cdot 1 0^{- 3})

lo g_{10} (lo g_{10} (10000 0^{2 x}))

\frac{ln ( \frac{9}{1024} )}{2 ln ( \frac{243}{16} )}

lo g_{10} (\frac{y z ^{3}}{x ^{5}})

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

What is simplify-3(1/2 ln(2^2-9)-1/2 ln((-2)^2-9)) ?
The solution to simplify-3(1/2 ln(2^2-9)-1/2 ln((-2)^2-9)) is 0