What is ln(sqrt(x^2+7)+1)+7ln(sqrt(x^2+7)-7) ?

The solution to ln(sqrt(x^2+7)+1)+7ln(sqrt(x^2+7)-7) is ln((sqrt(x^2+7)+1)(sqrt(x^2+7)-7)^7)

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simplify ln(sqrt(x^2+7)+1)+7ln(sqrt(x^2+7)-7)

simplify

ln (x^{2} + 7 + 1) + 7 ln (x^{2} + 7 - 7)

ln ((x^{2} + 7 + 1) (x^{2} + 7 - 7)^{7})

Solution steps

ln (x^{2} + 7 + 1) + 7 ln (x^{2} + 7 - 7)

Apply log rule:

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

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

= ln (x^{2} + 7 + 1) + ln ((x^{2} + 7 - 7)^{7})

Apply log rule:

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

ln (x^{2} + 7 + 1) + ln ((x^{2} + 7 - 7)^{7}) = ln ((x^{2} + 7 - 7)^{7} (x^{2} + 7 + 1))

= ln ((x^{2} + 7 + 1) (x^{2} + 7 - 7)^{7})

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ln (\frac{1}{499})

ln (17 e)

- lo g_{10} (4.6 \cdot 1 0^{- 5})

5 ln 1 0^{x} (2 x^{6} + 2)^{2} + 9 ln 7 x^{2} - 8

What is ln(sqrt(x^2+7)+1)+7ln(sqrt(x^2+7)-7) ?
The solution to ln(sqrt(x^2+7)+1)+7ln(sqrt(x^2+7)-7) is ln((sqrt(x^2+7)+1)(sqrt(x^2+7)-7)^7)