.
Answer. x = 1.
Solution
Introduce new variable u = .
Then your equation takes the form
u - 45/u + 4 = 0,
u^2 + 4u - 45 = 0,
(u-5)*(u+9) = 0
The last equation has two roots u= 5 and u= -9,
but since u = , only positive "u" works.
Thus u = 5, = 5 and x = 1.
Solved.
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Introducing new variable is the STANDARD method of solving exponential equations.
See the lesson
- Solving exponential equations
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Exponential equations".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.