What is ln((tx)^2)-2ln(ty) ?

The solution to ln((tx)^2)-2ln(ty) is ln((x^2)/(y^2))

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simplify ln((tx)^2)-2ln(ty)

simplify

ln ((t x)^{2}) - 2 ln (t y)

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

Solution steps

ln ((t x)^{2}) - 2 ln (t y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (t y) = ln ((t y)^{2})

= ln ((t x)^{2}) - ln ((t y)^{2})

Apply log rule:

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

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

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

Simplify

\frac{( t x ) ^{2}}{( t y ) ^{2}} : \frac{x ^{2}}{y ^{2}}

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

e^{3} + ln (16 x)

ln (x) - ln ((x^{2} + 3 x + 2)^{2})

ln (x + 1) + ln (sin (y))

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

- lo g_{10} (4.8 \cdot 1 0^{- 3})

What is ln((tx)^2)-2ln(ty) ?
The solution to ln((tx)^2)-2ln(ty) is ln((x^2)/(y^2))