What is ln((x^2)/(sqrt(x^2-36))) ?

The solution to ln((x^2)/(sqrt(x^2-36))) is 2ln(x)-ln(sqrt(x^2-36))

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simplify ln((x^2)/(sqrt(x^2-36)))

simplify

ln (\frac{x ^{2}}{x ^{2} - 36})

2 ln (x) - ln (x^{2} - 36)

Solution steps

ln (\frac{x ^{2}}{x ^{2} - 36})

Apply log rule:

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

ln (\frac{x ^{2}}{x ^{2} - 36}) = ln (x^{2}) - ln (x^{2} - 36)

= ln (x^{2}) - ln (x^{2} - 36)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 2 ln (x) - ln (x^{2} - 36)

- lo g_{10} (6.37 \cdot 1 0^{- 9})

- \frac{2 ln ( 2 )}{- 2 ln ( 2 ) - 1}

- lo g_{10} (1.83 \cdot 1 0^{- 6})

2 (lo g_{6} (x) - 2 lo g_{6} (z)) + 3 lo g_{6} (w)

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

What is ln((x^2)/(sqrt(x^2-36))) ?
The solution to ln((x^2)/(sqrt(x^2-36))) is 2ln(x)-ln(sqrt(x^2-36))