SOLUTION: 5^n+3/25^2n-3=1

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Question 1100166: 5^n+3/25^2n-3=1
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
In this form your formulas are  UNREADABLE.

Use parentheses to show and represent correctly  EVERY  TERM  of your equation.


USING  PARENTHESES  IS  a  MANDATORY  REQUIREMENT  OF  THIS  FORUM.



Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
My guess is that you meant
5^(n+3)/25^(2n-3)=1 or 5%5E%28n%2B3%29%2F25%5E%282n-3%29=1 .

Maybe this way to "show your work" would be accepted.
5%5E%28n%2B3%29%2F25%5E%282n-3%29=1
5%5E%28n%2B3%29=25%5E%282n-3%29
5%5E%28n%2B3%29=%285%5E2%29%5E%282n-3%29
5%5E%28n%2B3%29=5%5E%284n-6%29
Maybe you would guess
(or maybe you understand why, and really know)
that the only solution will come from
n%2B3=4n-6
3%2B6=4n-n
9=3n
n=9%2F3
n=3

Some teacher may prefer
5%5E%28n%2B3%29%2F25%5E%282n-3%29=1
5%5E%28n%2B3%29%2F%285%5E2%29%5E%282n-3%29=1
5%5E%28n%2B3%29%2F5%5E%284n-6%29=1
5%5E%28%28n%2B3%29-%284n-6%29%29=1
5%5E%28n%2B3-4n%2B6%29=1
5%5E%28-3n%2B9%29=1
-3n%2B9=0
9=3n
n=9%2F3
n=3

I read 5^n+3/25^2n-3=1 as
5%5En%22%2B%223%2F25%5E%222+n%22-3%22=%221 <--> 5%5En%22%2B%223%2F25%5E%222+n%22%22=%224 ,
and for that problem, n=0 is an obvious solution.
Calculus tells me that here is another solution,
and you could find 0.8595 as an approximation for that solution
using a graphing calculator.

NOTE:
When you are typing math,
here or on a calculator or computer,
you need to make sure you have parentheses where they are needed.
To avoid misunderstandings,
people need to communicate in the same language.
Almost all calculators, all computers, and many people
talk/understand algebra,
and use the order-of-operations conventions.
Those conventions make it possible to understand each other
when we write complex algebraic expression with pen or pencil.
Those conventions were needed to go from one-operation-at-a-time
to more or less complex formulas.

There are implied parentheses
in the way we write some expressions with pen or pencil on paper,
and we need to type them when we type algebraic expressions.
%28100-1%29%2F%28100-1%29 should be typed as (100-1)/(100-1),
because typing 100-1/100-1 means
100-1%2F100-1=100-0.01-1=98.99
and I bet your calculator knows that.
5%5E%282n-3%29 should be typed as 5^(2n-3).
Early in their life children learn to say one word at a time.
A child could say "bite, dog" and an adult may try to guess what they meant.
Later, they figure out how to arrange several words into phrases,
and if a child says "a dog bit me,"
using the proper conventions of English grammar,
an adult would understand, and may promptly take the child to a doctor.