1. Simplify frac{left(x^{3}+xright) sinh left(4 log _{e}(x)right)}{left(x^{4}+1right) sinh left(log _{e}(x)right.} for x0.

Question

1. Simplify frac{left(x^{3}+xright) sinh left(4 log _{e}(x)right)}{left(x^{4}+1right) sinh left(log _{e}(x)right.} for x>0.

Accepted Answer

Step:1 ：Rewrite the expression using natural logarithm notation (ln) instead of log base e: (frac{left(x^{3}+xright) sinh left(4 ln(x)right)}{left(x^{4}+1right) sinh left(ln(x)right)}) for (x>0)Step:2 ：Use the property of logarithms: (nln(x) = ln(x^n))Step:3 ：Use the property of hyperbolic functions: (sinh(a+b) = sinh(a)cosh(b) + cosh(a)sinh(b))Step:4 ：(frac{xleft(x^{2}+1right) sinh left(4 ln(x)right)}{left(x^{4}+1right) sinh left(ln(x)right)})Step:5 ：(boxed{frac{xleft(x^{2}+1right) sinh left(4 ln(x)right)}{left(x^{4}+1right) sinh left(ln(x)right)}})

Answer

Step: 1 ：Rewrite the expression using natural logarithm notation (ln) instead of log base e: (frac{left(x^{3}+xright) sinh left(4 ln(x)right)}{left(x^{4}+1right) sinh left(ln(x)right)}) for (x>0)Step: 2 ：Use the property of logarithms: (nln(x) = ln(x^n))Step: 3 ：Use the property of hyperbolic functions: (sinh(a+b) = sinh(a)cosh(b) + cosh(a)sinh(b))Step: 4 ：(frac{xleft(x^{2}+1right) sinh left(4 ln(x)right)}{left(x^{4}+1right) sinh left(ln(x)right)})Step: 5 ：(boxed{frac{xleft(x^{2}+1right) sinh left(4 ln(x)right)}{left(x^{4}+1right) sinh left(ln(x)right)}})

1. Simplify $\frac{(x^{3} + x) \sinh (4 \log_{e} (x))}{(x^{4} + 1) \sinh (\log_{e} (x)}$ for $x > 0$ .

Answer

Popular Problems

1. Simplify (x3+x)sinh⁡(4loge⁡(x))(x4+1)sinh⁡(loge⁡(x) for x>0.

Answer

Popular Problems

1. Simplify $\frac{(x^{3} + x) \sinh (4 \log_{e} (x))}{(x^{4} + 1) \sinh (\log_{e} (x)}$ for $x > 0$ .