What is ln(7x(cos(x))^{x/2}) ?

The solution to ln(7x(cos(x))^{x/2}) is ln(7)+ln(x)+(xln(cos(x)))/2

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simplify ln(7x(cos(x))^{x/2})

simplify

ln (7 x (cos (x))^{\frac{x}{2}})

ln (7) + ln (x) + \frac{x ln ( cos ( x ) )}{2}

Solution steps

ln (7 x (cos (x))^{\frac{x}{2}})

Apply log rule:

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

ln (7 x cos^{\frac{x}{2}} (x)) = ln (7) + ln (x) + ln (cos^{\frac{x}{2}} (x))

= ln (7) + ln (x) + ln (cos^{\frac{x}{2}} (x))

Apply log rule:

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

ln (cos^{\frac{x}{2}} (x)) = \frac{x}{2} ln (cos (x))

= ln (7) + ln (x) + \frac{x}{2} ln (cos (x))

Multiply

\frac{x}{2} ln (cos (x)) : \frac{x ln ( cos ( x ) )}{2}

= ln (7) + ln (x) + \frac{x ln ( cos ( x ) )}{2}

lo g_{10} (a + b) - lo g_{10} (a) - lo g_{10} (b)

lo g_{10} (\frac{k}{r})

4 lo g_{10} (a) - \frac{1}{2} lo g_{10} (b) + lo g_{10} (c)

ln (e^{19} x^{20})

lo g_{10} (\frac{x ^{3} ( x + 3 )}{( x - 1 ) x + 5})

What is ln(7x(cos(x))^{x/2}) ?
The solution to ln(7x(cos(x))^{x/2}) is ln(7)+ln(x)+(xln(cos(x)))/2