Question

125^x+1 * 23^x+1=2500

Answer 1

i have started it..may i know am i going right??
\[5^{3x+3} \times 23^{x+1} = 50^{2}\]

Answer 2

Going back to the beginning:
That is 125^(x+1) * 23^(x+1) = 2500
correct?

Answer 3

yaa correct @wolf1728

Answer 4

So, basically if x = .9825 then
it equals 2500.9884533405

Answer 5

how did you get that?? i cant understand??

Answer 6

Just doing a few calculations - trial and error.
I always like to get a rough idea before doing any serious equation solving.

Answer 7

125^.9825 = 114.8719749473
23^.9825 = 21.7719635663

114.8719749473 * 21.7719635663 =
2500.9884533405

Answer 8

I think this is a logarithm question.

Answer 9

See:

\[\large{125^{x+1} \times 23^{x+1} = 2500}\]
\[\large{\implies 5^{3x+3} \times 23^{x+1} = 50^2}\]

Taking log base 10 both sides,

\[\large{\implies (3x+3)\log5 + (x+1)\log23 = 2\log50}\]
\[\large{\implies (3x+3)\log5 + (x+1)\log23 = 2\log(5^2\times 2)}\]
\[\large{\implies (3x+3)\log5 + (x+1)\log23 = 2(2\log 5 + \log2)}\]
\[\large{\implies (3x+3)\log5 + (x+1)\log23 = 4\log5 + 2\log2}\]
\[\large{\implies (3x-1)\log5 + (x+1)\log23 = 2\log2}\]
\[\large{\implies 3x\log5 + x\log23 -\log5 + \log23 = 2\log2}\]
\[\large{\implies x(3\log5+\log23) = 2\log2 + \log5 - \log23}\]
\[\large{\implies x = \cfrac{2\log2+\log5 - \log23}{3\log5+\log23}}\]

Now, using a calculator find out the value of x.

Answer 10

@dinisha , I hope this helps you.

Answer 11

Ask me if you don't understand any step.

Answer 12

I thought I was good at logarithms but that was one heck of a solution you did there!!

Answer 13

:)

Answer 14

I just ignored those "+1" terms in the exponents thinking they were totally inconsequential.

Answer 15

2*log(2) = 0.6020599913
log(5) = 0.6989700043
-log(23) = -1.361727836

Numerator SUM = -0.0606978404

3 * log(5) = 2.096910013
log(23) = 1.361727836

Denominator Sum = 3.458637849

Numerator / Denominator = -0.0175496375

(not quite .9825 is it???)

Answer 16

Perfectly correct calculation @wolf1728 :)

Answer 17

Even wolfram agrees with you.

So, x = -0.0175... and that's correct :)

Answer 18

Oh geez - I just thought of the actual STUPID answer. After all those calculations and exponentiations, etc - I actually (with .9825) solved for X PLUS 1 .
So the answer really is
.9825 = X PLUS 1 or -.0175
How foolish of me to forget i was solving for X PLUS 1.
Geez couldd they make this any more complicated ?????

Answer 19

:) Well I really have some sympathy for you

That happens a lot..

Answer 20

Thanks - and thanks for the medal - even though you found the actual answer (and not the trial and error solution).
Once again, good work vishweshshrimali5 !!!

Answer 21

Thanks and same to you @wolf1728. Trying is much more important than finding the correct answer. :)

Good day

Answer 22

Guess so
:-)

Answer 23

but the answer provided are 5/4 or 1/4 or 3/4 or 2/3 or 1/3 .. even when i convert the answer into fraction its not similar to anything @vishweshshrimali5 and @wolf1728