What is 7log_{e}(x)-0.5log_{e}(y) ?

The solution to 7log_{e}(x)-0.5log_{e}(y) is ln((x^7)/(y^{0.5)})

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simplify 7log_{e}(x)-0.5log_{e}(y)

simplify

7 lo g_{e} (x) - 0.5 lo g_{e} (y)

ln (\frac{x ^{7}}{y ^{0.5}})

Solution steps

7 lo g_{e} (x) - 0.5 lo g_{e} (y)

Apply log rule:

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

7 lo g_{e} (x) = lo g_{e} (x^{7})

= lo g_{e} (x^{7}) - 0.5 lo g_{e} (y)

Apply log rule:

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

0.5 lo g_{e} (y) = lo g_{e} (y^{0.5})

= lo g_{e} (x^{7}) - lo g_{e} (y^{0.5})

Apply log rule:

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

lo g_{e} (x^{7}) - lo g_{e} (y^{0.5}) = lo g_{e} (\frac{x ^{7}}{y ^{0.5}})

= lo g_{e} (\frac{x ^{7}}{y ^{0.5}})

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (\frac{x ^{7}}{y ^{0.5}})

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

ln (4 e^{- \frac{6}{100} t})

20 e^{9} + ln (12) + 50 - ln (9)

- lo g_{10} (2.3 \cdot 1 0^{- 9})

ln (\frac{1}{2 ^{n}} \cdot e^{- 2 x} e^{- 3 t})

What is 7log_{e}(x)-0.5log_{e}(y) ?
The solution to 7log_{e}(x)-0.5log_{e}(y) is ln((x^7)/(y^{0.5)})