What is ln(x^2)-ln(y^2)+ln(l^2) ?

The solution to ln(x^2)-ln(y^2)+ln(l^2) is ln((l^2x^2)/(y^2))

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simplify ln(x^2)-ln(y^2)+ln(l^2)

simplify

ln (x^{2}) - ln (y^{2}) + ln (l^{2})

ln (\frac{l ^{2} x ^{2}}{y ^{2}})

Solution steps

ln (x^{2}) - ln (y^{2}) + ln (l^{2})

Apply log rule:

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

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

= ln (\frac{x ^{2}}{y ^{2}}) + ln (l^{2})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{x ^{2}}{y ^{2}}) + ln (l^{2}) = ln (l^{2} \frac{x ^{2}}{y ^{2}})

= ln (l^{2} \frac{x ^{2}}{y ^{2}})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{l ^{2} x ^{2}}{y ^{2}})

lo g_{10} ((\frac{1}{4})_{2}) + 1

ln (8) - ln (e^{y})

ln (\frac{343}{293})

ln (\frac{∣ Bl - E ∣}{∣ E ∣})

lo g_{2} (0.7) \cdot 0.7 + lo g_{2} (0.3) \cdot 0.3

What is ln(x^2)-ln(y^2)+ln(l^2) ?
The solution to ln(x^2)-ln(y^2)+ln(l^2) is ln((l^2x^2)/(y^2))