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Popular >

simplify ln(xe^{(y/z)})

Solution

simplify

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

Solution

ln (x) + \frac{y}{z}

Solution steps

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

Apply log rule:

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

ln (x e^{(\frac{y}{z})}) = ln (x) + ln (e^{(\frac{y}{z})})

= ln (x) + ln (e^{(\frac{y}{z})})

Apply log rule:

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

ln (e^{(\frac{y}{z})}) = \frac{y}{z} ln (e)

= ln (x) + \frac{y}{z} ln (e)

\frac{y}{z} ln (e) = \frac{y}{z}

= ln (x) + \frac{y}{z}

Popular Examples

simplify-(ln(9/2)-ln(25/2))/4 simplify

- \frac{ln ( \frac{9}{2} ) - ln ( \frac{25}{2} )}{4}

simplify-log_{10}(1.4*10^{-6})simplify

- lo g_{10} (1.4 \cdot 1 0^{- 6})

simplify 20/100*ln(20/100)simplify

\frac{20}{100} \cdot ln (\frac{20}{100})

expand log_{3}(3x^3y^5)expand

lo g_{3} (3 x^{3} y^{5})

simplify 1/2 ln((-2)/2)simplify

\frac{1}{2} ln (\frac{- 2}{2})

Frequently Asked Questions (FAQ)

What is ln(xe^{(y/z)}) ?
The solution to ln(xe^{(y/z)}) is ln(x)+y/z