Answer to Question #102450 in Algebra for Glory okoli

Question

Solve for x from: 2x^log³4+3^log^x4=27

Answer 1

Solution. Consider the value

$$log 4\approx 0.602$$

Therefore functions

$$2x^{log^34}=2x^{0.2182}$$

and

$$3^{log^x4}=3^{0.602^x}$$

Sketch of the function

$$2x^{0.2182}+3^{0.602^x}$$

and find at what values of the argument for which the value of the function is 27.

As result get x=127240.

Answer. x=127240