Please solve this for me

Question

https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=16989867092833707686

Answer 1

x= 1.1868

For complete solution see the link below

https://ibb.co/HqxpTX6

Comments

Very well done.

I came up later with the same result and I was just about to expand my earlier answer when I saw your solution. I adopted a similar approach when I had more time to study it: ln((√5-1)/2)/ln(⅔).

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Thank  You Sir.

Answer 2

x=1.18681439028 approx.

Let y=4ˣ+6ˣ-9ˣ, then dy/dx=4ˣln(4)+6ˣln(6)-9ˣln(9).

A graph of y shows an x-intercept near x=1.

Substitute x in:

x-(4ˣ+6ˣ-9ˣ)/(4ˣln(4)+6ˣln(6)-9ˣln(9)).

This gives us another value of x to plug into the expression (Newton’s Method).

Repeat the exercise until the same value of x is repeated (limited by calculator).