convert-the-expression-x5lnxxfrac5ln-x-to-base-e-when-0x-and-gt0x-and-gt-0-and-x

Question

Express the expression $k^{\frac{3}{\ln k}}$ in terms of the natural base e, for $k > 0$ and $k ≠ 1$ .

Accepted Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>e</mi><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">e^3</annotation></semantics></math>e3﻿

Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>k</mi><mrow><mi>ln</mi><mo>⁡</mo><mi>e</mi></mrow></msup></mrow><annotation encoding="application/x-tex">k^{\ln e}</annotation></semantics></math>klne﻿

Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>e</mi><mfrac><mn>3</mn><mrow><mi>ln</mi><mo>⁡</mo><mi>k</mi></mrow></mfrac></msup></mrow><annotation encoding="application/x-tex">e^{\frac{3}{\ln k}}</annotation></semantics></math>elnk3​﻿

Answer

﻿<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>k</mi><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">k^3</annotation></semantics></math>k3﻿

Express the expression k3lnkk^{\frac{3}{\ln k}}klnk3 in terms of the natural base e, for k>0k > 0k>0 and k≠1k ≠ 1k=1.

Express the expression $k^{\frac{3}{\ln k}}$ in terms of the natural base e, for $k > 0$ and $k ≠ 1$ .