What is ln((ty)/(tx)) ?

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

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simplify ln((ty)/(tx))

simplify

ln (\frac{t y}{t x})

ln (y) - ln (x)

Solution steps

ln (\frac{t y}{t x})

Apply log rule:

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

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

= ln (t y) - ln (t x)

Apply log rule:

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

ln (t y) = ln (t) + ln (y), ln (t x) = ln (t) + ln (x)

= ln (t) + ln (y) - (ln (t) + ln (x))

- (ln (t) + ln (x)) : - ln (t) - ln (x)

= ln (t) + ln (y) - ln (t) - ln (x)

Simplify

ln (t) + ln (y) - ln (t) - ln (x) : ln (y) - ln (x)

= ln (y) - ln (x)

lo g_{10} (316) + 3 lo g_{10} (8 (5)) - 2.92

- lo g_{10} (6 \cdot 1 0^{- 8})

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

lo g_{7} (\frac{3 ^{6}}{5 \cdot 8 ^{4}})

ln (\frac{- v ^{2}}{2 α e ^{- β s}})