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Popular >

simplify ln((x*y)/(e^1))

Solution

simplify

ln (\frac{x \cdot y}{e ^{1}})

Solution

ln (x) + ln (y) - 1

Solution steps

ln (\frac{x y}{e ^{1}})

Apply log rule:

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

ln (\frac{x y}{e ^{1}}) = ln (x y) - ln (e^{1})

= ln (x y) - ln (e^{1})

Apply log rule:

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

ln (e^{1}) = 1 \cdot ln (e)

= ln (x y) - 1 \cdot ln (e)

Apply log rule:

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

ln (x y) = ln (x) + ln (y)

= ln (x) + ln (y) - 1 \cdot ln (e)

1 \cdot ln (e) = 1

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

Popular Examples

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Frequently Asked Questions (FAQ)

What is ln((x*y)/(e^1)) ?
The solution to ln((x*y)/(e^1)) is ln(x)+ln(y)-1