Question

log x power 2 .base 3 = 2 find x=?​

Answer 1

Hola Mate ❤

( 3 to the power log x base 3 ) + ( x to the power log x base 3 ) = 162 , what is x ? You mean 3log3 ( x ) + xlog3 ( x ) = 162 . But 3l0g3 ( x ) = x and log2 ( xlog3 ( x ) ) = ( log ( 3 ) ) 2 . Therefore ælog3 ( x ) = 3 ( logą ( 3 ) ) . Let y = log2 ( x ) , then 34 + 39 ' = 162 . This clearly has two solutions , y a little more than 2 and y a little less than - 2 . I . e . X is a little more than 9 or x is a little less then 1 / 9 . To solve this you will need to use numerical approximations . The simplest method is repeated bisection . Find 39 + 39 " when y = 2 and when y = 3 . One is smaller than 162 , and one is greater . Take the average . At each step you get an interval surrounding the answer . Keep bisecting the interval between the two closest approximations until the answer is accurate enough for your purposes .