Question

log((x(sqrtã(X^2+1)/(x+1)^(2/3)))^6

Any ideas would be great, thanks

Answer 1

that should be x times the square root of x squared plus one divided by( or fraction bar) x plus one raised to the 2/3 power, all raised to the power of 6

Answer 2

You will have to know the 3 main rules of logs
log (AB) = logA + logB
log(A/B) = logA - logB
log A^n = nlogA

so the outer exponent 6 can be brought down immediately to ge

6log(x√(x^2 + 1)/(x+1)^(2/3) )
= 6 ( logx + (1/2)log(x^2 + 1) - (2/3)log(x+1) )
= 6logx + 3log(x^2 + 1) - 4log(x+1)