What is ln((x^2)/(e^{sqrt(x)cos(x))}) ?

The solution to ln((x^2)/(e^{sqrt(x)cos(x))}) is 2ln(x)-sqrt(x)cos(x)

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simplify ln((x^2)/(e^{sqrt(x)cos(x))})

simplify

ln (\frac{x ^{2}}{e ^{x c o s (x)}})

2 ln (x) - x cos (x)

Solution steps

ln (\frac{x ^{2}}{e ^{x c o s (x)}})

Apply log rule:

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

ln (\frac{x ^{2}}{e ^{x c o s (x)}}) = ln (x^{2}) - ln (e^{x c o s (x)})

= ln (x^{2}) - ln (e^{x c o s (x)})

Apply log rule:

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

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

= 2 ln (x) - ln (e^{x c o s (x)})

Apply log rule:

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

ln (e^{x c o s (x)}) = x cos (x) ln (e)

= 2 ln (x) - x cos (x) ln (e)

x cos (x) ln (e) = x cos (x)

= 2 ln (x) - x cos (x)

lo g_{8} (\frac{x ^{3}}{5})

lo g_{10} (x) + lo g_{10} (x + 3) - 2 lo g_{10} (x + 1)

- \frac{1}{3} + \frac{1}{3} ln (\frac{3 + 5}{2})

3 ln (2) - 2 ln (3)

\frac{6 ln ( 3 ) - 10 ln ( 2 )}{2}

What is ln((x^2)/(e^{sqrt(x)cos(x))}) ?
The solution to ln((x^2)/(e^{sqrt(x)cos(x))}) is 2ln(x)-sqrt(x)cos(x)