What is 1/2 ln(7^2-9)-1/2 ln(5^2-9) ?

The solution to 1/2 ln(7^2-9)-1/2 ln(5^2-9) is ln((sqrt(10))/2)

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simplify 1/2 ln(7^2-9)-1/2 ln(5^2-9)

simplify

\frac{1}{2} ln (7^{2} - 9) - \frac{1}{2} ln (5^{2} - 9)

ln (\frac{10}{2})

Decimal Notation

0.45814 \dots

Solution steps

\frac{1}{2} ln (7^{2} - 9) - \frac{1}{2} ln (5^{2} - 9)

Apply log rule:

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

\frac{1}{2} ln (7^{2} - 9) = ln ((7^{2} - 9)^{\frac{1}{2}})

= ln ((7^{2} - 9)^{\frac{1}{2}}) - \frac{1}{2} ln (5^{2} - 9)

Apply log rule:

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

\frac{1}{2} ln (5^{2} - 9) = ln ((5^{2} - 9)^{\frac{1}{2}})

= ln ((7^{2} - 9)^{\frac{1}{2}}) - ln ((5^{2} - 9)^{\frac{1}{2}})

Apply log rule:

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

ln ((7^{2} - 9)^{\frac{1}{2}}) - ln ((5^{2} - 9)^{\frac{1}{2}}) = ln \frac{( 7 ^{2} - 9 ) ^{\frac{1}{2}}}{( 5 ^{2} - 9 ) ^{\frac{1}{2}}}

= ln \frac{( 7 ^{2} - 9 ) ^{\frac{1}{2}}}{( 5 ^{2} - 9 ) ^{\frac{1}{2}}}

\frac{( 7 ^{2} - 9 ) ^{\frac{1}{2}}}{( 5 ^{2} - 9 ) ^{\frac{1}{2}}} = \frac{10}{2}

= ln (\frac{10}{2})

- 500 ln (\frac{500}{1000 + 50})

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\frac{1}{2} ln ∣ 2 x + 1 ∣ + 2 ln ∣ x - 1 ∣

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- lo g_{10} (1.8 \cdot 1 0^{- 15})

What is 1/2 ln(7^2-9)-1/2 ln(5^2-9) ?
The solution to 1/2 ln(7^2-9)-1/2 ln(5^2-9) is ln((sqrt(10))/2)