What is ln((ex^6)/y) ?

The solution to ln((ex^6)/y) is 1+6ln(x)-ln(y)

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simplify ln((ex^6)/y)

simplify

ln (\frac{e x ^{6}}{y})

1 + 6 ln (x) - ln (y)

Solution steps

ln (\frac{e x ^{6}}{y})

Apply log rule:

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

ln (\frac{e x ^{6}}{y}) = ln (e x^{6}) - ln (y)

= ln (e x^{6}) - ln (y)

Apply log rule:

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

ln (e x^{6}) = ln (e) + ln (x^{6})

= ln (e) + ln (x^{6}) - ln (y)

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= ln (e) + 6 ln (x) - ln (y)

Apply log rule:

lo g_{a} (a) = 1

= 1 + 6 ln (x) - ln (y)

2 lo g_{2} (x) + 4 lo g_{2} (y)

(lo g_{10} (6) + lo g_{10} (4)) - lo g_{10} (3)

2 lo g_{10} (5) - 6 lo g_{10} (3)

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

(\frac{1}{e})^{2} lo g_{3} (\frac{1}{e})