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4log2 (3) + 2log2(5)= log2 (3)^4 + log2 (5)^2= log2 (3^4x5^2)=log2(81x25)=log2(2025)
The solution will be explained with the formula for- loga(x) +loga(y)=loga(xy)





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a^m+n

let u = sin(x) and v = cos(x) => z = u/v. The quoitent rule is (u'v - v'u)/v^2, where u' = du/dx, v' = dv/dx. In this case du/dx = cos(x) and dv/dx = -sin(x) => u'v = cos^2(x) and v'u = -sin^2(x) =&...

You first develop the expression on the left side of the equation:(sin(T)+cos(T))(1-sin(T)cos(T))=sin(T)-sin^2(T)cos(T)+cos(T)-sin(T)cos^2(T)=sin(T)(1-cos^2(T))+cos(T)(1-sin^2(T))Now, you will need to use...

Differentiate U with respect to x to find dx in terms of du and substitute into the integral so that it is in terms of du, then using e^3x = (e^x)^3 and u = 1+e^x subsitute u in for x and simplify the int...