What is ln((x^2)/(sqrt(4x+1))) ?

The solution to ln((x^2)/(sqrt(4x+1))) is 2ln(x)-ln(sqrt(4x+1))

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simplify ln((x^2)/(sqrt(4x+1)))

simplify

ln (\frac{x ^{2}}{4 x + 1})

2 ln (x) - ln (4 x + 1)

Solution steps

ln (\frac{x ^{2}}{4 x + 1})

Apply log rule:

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

ln (\frac{x ^{2}}{4 x + 1}) = ln (x^{2}) - ln (4 x + 1)

= ln (x^{2}) - ln (4 x + 1)

Apply log rule:

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

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

= 2 ln (x) - ln (4 x + 1)

lo g_{10} (16 x^{2}) + 2 lo g_{10} (\frac{1}{x})

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

lo g_{b} (\frac{7}{9})

lo g_{10} (8) + lo g_{10} (x)

ln (\frac{5}{100})

What is ln((x^2)/(sqrt(4x+1))) ?
The solution to ln((x^2)/(sqrt(4x+1))) is 2ln(x)-ln(sqrt(4x+1))