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Popular >

simplify ln(a*e^{(x^2)})

Solution

simplify

ln (a \cdot e^{(x^{2})})

Solution

ln (a) + x^{2}

Solution steps

ln (a e^{(x^{2})})

Apply log rule:

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

ln (a e^{(x^{2})}) = ln (a) + ln (e^{(x^{2})})

= ln (a) + ln (e^{(x^{2})})

Apply log rule:

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

ln (e^{(x^{2})}) = x^{2} ln (e)

= ln (a) + x^{2} ln (e)

x^{2} ln (e) = x^{2}

= ln (a) + x^{2}

Popular Examples

simplify 3ln(4)+ln(2^7)simplify

3 ln (4) + ln (2^{7})

simplify 2ln(3^4)+ln(3^3)-ln(9)simplify

2 ln (3^{4}) + ln (3^{3}) - ln (9)

simplify log_{10}((1-p)^x*p)simplify

lo g_{10} ((1 - p)^{x} \cdot p)

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ln (\frac{1 + x}{y})

simplify 4.76+log_{10}((11)/(4.8))simplify

4.76 + lo g_{10} (\frac{11}{4.8})

Frequently Asked Questions (FAQ)

What is ln(a*e^{(x^2)}) ?
The solution to ln(a*e^{(x^2)}) is ln(a)+x^2