What is ln((ex^4)/y) ?

The solution to ln((ex^4)/y) is 1+4ln(x)-ln(y)

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simplify ln((ex^4)/y)

simplify

ln (\frac{e x ^{4}}{y})

1 + 4 ln (x) - ln (y)

Solution steps

ln (\frac{e x ^{4}}{y})

Apply log rule:

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

ln (\frac{e x ^{4}}{y}) = ln (e x^{4}) - ln (y)

= ln (e x^{4}) - ln (y)

Apply log rule:

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

ln (e x^{4}) = ln (e) + ln (x^{4})

= ln (e) + ln (x^{4}) - ln (y)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{4}) = 4 ln (x)

= ln (e) + 4 ln (x) - ln (y)

Apply log rule:

lo g_{a} (a) = 1

= 1 + 4 ln (x) - ln (y)

\frac{1}{2} lo g_{10} (a) + 6 lo g_{10} (b)

8 ln (x) - \frac{1}{7} ln (y)

- \frac{4}{10} lo g_{2} (\frac{4}{10}) - \frac{6}{10} lo g_{2} (\frac{6}{10})

ln (\frac{3 x - 5}{7})

lo g_{49} (\frac{20000}{50}) + 1