What is ln(8+sqrt(65))-ln(sqrt(65)-8) ?

The solution to ln(8+sqrt(65))-ln(sqrt(65)-8) is ln(129+16sqrt(65))

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simplify ln(8+sqrt(65))-ln(sqrt(65)-8)

simplify

ln (8 + 65) - ln (65 - 8)

ln (129 + 1665)

Decimal Notation

5.55294 \dots

Solution steps

ln (8 + 65) - ln (65 - 8)

Apply log rule:

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

ln (8 + 65) - ln (65 - 8) = ln (\frac{8 + 65}{65 - 8})

= ln (\frac{8 + 65}{65 - 8})

\frac{8 + 65}{65 - 8} = 129 + 1665

= ln (129 + 1665)

9 lo g_{8} (x) + 18 lo g_{8} (y)

lo g_{10} (\frac{x ( x + 4 )}{( x + 6 ) ^{9}})

lo g_{10} (x) - 4 lo g_{10} (y) + 2 lo g_{10} (z)

ln (\frac{( 3 b ^{2} + 21 b )}{( 11 b + 77 )})

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

What is ln(8+sqrt(65))-ln(sqrt(65)-8) ?
The solution to ln(8+sqrt(65))-ln(sqrt(65)-8) is ln(129+16sqrt(65))