Solving Exponential Equation @KasyannoEZMath

This tutorial video explains how to solve the given exponential equation.
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[kurtsopa]

You can get the answer in three easy steps by converting everything to base 5. That is, 5^x + 5^2x = 5^2+ 5^4. Then add the exponentials, x + 2x = 2 + 4, which equals to 3x = 6, and therefore x = 2.

[nikolayguzman]

25**x
x=1
25**1=25
25**2=625
25**3 >> than 650
Therefore 1<x<3
Result x=2

[wallstreetoneil]

A Quadratic in 5^x - using quadratic formula you get 5^x = (-1 + (1 + 4x650)^.5) / 2 => (-1+(2601)^.5)/2 => (-1+(3^2*17^2)^.5)/2 => (-1 + 3x17)/2 => (-1 + 51)/2 => 25. Thus 5^x = 25 or x=log(base5)25 =2

[larisamedovaya]

Let 5^x=y; then y^2+y-650=0; solve quadratic equation: restriction : y>0 since 5^x can’t be 0 or less; 5^x=5^2;x=2; GED

[JoseAraujo-wowe]

From what the video already indicates 5^x=25 => x=2
The other solution is missing, 5^x=-26
Applying natural logarithm:
ln(5^x)=ln(-26) => x.ln(5)=ln(-26) => x=ln(-26)/ln(5), now
ln(-26)=ln(-1*26)=ln(-1)+ln(26),
If ln(-1)=c, by definition => e^c=-1 => e^c+1=0, by Euler's identity
c = πi
The other solution on complex numbers is x=(ln(26)+πi)/ln(5)

[guitarttimman]

You can also use Logarithms to get x = 2.

[ajushahul]

You can get the answer in 30sec without any pen or paper

[Hello-mxne]

I would like to know can I get the points if I directly answer 2.

[noirjacques]

I knew the answers to both squares anyway, hence just add 25+625. Unrelated, if anyone wants to test themselves on squared numbers, the easiest way (without a calculating device) is start at 1 then progressively add each odd number. 1+3=2Sq;
1+3+5=3sq;1+3+5+7=4sq… etc.

[musicsubicandcebu]

Factor the LHS . . . 5²(1+5²) = 5²(1+5² )

[TheFlax]

Quick tip for quadratics====Find factors reverse there sign =

[Aposefendi]

hello, as I see it, I understood that it is 2, there is no need for that much process, it can be done by guessing and trying

[victorgloria]

To shorten the solution, use binomial factoring instead of the longer factoring by grouping. Try to compare these two approaches.

[equus]

by permutation & combination value of x = 2.

[Extra-]

It's easy method 5^x + 5^2x = 5^4 + 5^2
Base same so,
x + 2x = 4 + 2
3x = 6
x = 6/3
x = 2, Answer

[TheFlax]

Very good method of teaching (whole) problems. Thanks.

[lounar]

If we do log base 5 (650) we get 5^4.024. When we now equate the two sides which are now each in base five, we get 3x=4.024. But it doesn't work...how come??

[jyotshnamakthal]

X is 2.
5^x + 25^x = 650.
5^2 + 25^2 = 25+625=650.

[bvideoz]

3:49 I do not understand - why didn't you just solve the quadratic quation? I mean why did you have to over-complicate it, the quadratic equation is easily solvable 🤪

[dersdersdeers]

Dude just use logarithmic functions. Add log 5 both sides bam