What is ln(7x^2-5)-ln(x^2) ?

The solution to ln(7x^2-5)-ln(x^2) is ln((7x^2-5)/(x^2))

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simplify ln(7x^2-5)-ln(x^2)

simplify

ln (7 x^{2} - 5) - ln (x^{2})

ln (\frac{7 x ^{2} - 5}{x ^{2}})

Solution steps

ln (7 x^{2} - 5) - ln (x^{2})

Apply log rule:

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

ln (7 x^{2} - 5) - ln (x^{2}) = ln (\frac{7 x ^{2} - 5}{x ^{2}})

= ln (\frac{7 x ^{2} - 5}{x ^{2}})

\frac{1}{2} ln (\frac{386}{530})

3 ln (3) - 6 ln (2)

120 + 10 lo g_{10} (\frac{1}{4 \cdot 3.14 \cdot 100}) + 10

lo g_{10} (5 x) + lo g_{7} (x)

3 ln (\frac{10 + 104}{2})

What is ln(7x^2-5)-ln(x^2) ?
The solution to ln(7x^2-5)-ln(x^2) is ln((7x^2-5)/(x^2))