What is the answer to roots ln(x+sqrt(a^2+x^2)) ?

The answer to roots ln(x+sqrt(a^2+x^2)) is x=-(a^2-1)/2

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roots ln(x+sqrt(a^2+x^2))

roots

ln (x + a^{2} + x^{2})

x = - \frac{a ^{2} - 1}{2}

Solution steps

ln (x + a^{2} + x^{2})

The roots are the intercepts with the x-axis

(y = 0)

ln (x + a^{2} + x^{2}) = 0

Apply log rules

x + a^{2} + x^{2} = 1

Solve

x + a^{2} + x^{2} = 1 : x = - \frac{a ^{2} - 1}{2}

x = - \frac{a ^{2} - 1}{2}

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

lo g_{10} (2 x) + lo g_{10} (x) = lo g_{10} (5) + 1

ln (x) + ln (x + 1) = 4

lo g_{\frac{1}{6}} (3 - 10 x) = - 2

lo g_{10} (3 x + 1) - lo g_{10} (2 x - 3) = 1 - lo g_{10} (5)

What is the answer to roots ln(x+sqrt(a^2+x^2)) ?
The answer to roots ln(x+sqrt(a^2+x^2)) is x=-(a^2-1)/2