25^(x-1)
=5^(2x-1)-100
find x please
tssuyambulingam:
what happened im sorry
look at RHS plzz
its5^(2x-1)
okkkkk
what happened
after solving it,my x is going to be cancelled out
try it once pls
your question's statement is false.plzz type clear statement
you know the answer?
I can try,match the answer
Answers
Answered by
533
25^x-1 = 5^(2x-1) - 100
⇒ 5^2x-2 = 5^(2x-1) - 100
⇒ 5^2x-2 - 5^2x-1 = -100
⇒ 5^2x [ 5^-2 - 5^-1] = - 100
⇒ 5^2x [ 1 - 1 ] = - 100
25 5
⇒ 5^2x [ 1 - 5] = - 100
25
⇒ 5^2x [ -4 ] = - 100
25
⇒ 5^2x [-4] = -100 * 25
⇒ 5^2x = 100 * 25 [ - * - = +]
4
⇒ 5^2x = 625
⇒ 5^2x = 5^4
so, ⇒ 2x = 4
⇒ x = 2
⇒ 5^2x-2 = 5^(2x-1) - 100
⇒ 5^2x-2 - 5^2x-1 = -100
⇒ 5^2x [ 5^-2 - 5^-1] = - 100
⇒ 5^2x [ 1 - 1 ] = - 100
25 5
⇒ 5^2x [ 1 - 5] = - 100
25
⇒ 5^2x [ -4 ] = - 100
25
⇒ 5^2x [-4] = -100 * 25
⇒ 5^2x = 100 * 25 [ - * - = +]
4
⇒ 5^2x = 625
⇒ 5^2x = 5^4
so, ⇒ 2x = 4
⇒ x = 2
but i cant understand the 4th step
when you do 5*5=25 but here the -square so.
ok thanks
now understand?
yes akka
:)
what
Answered by
385
we need to bring together the terms containing x. Then constant terms on the other side. Then simplify by performing the addition/subtraction/multiplication.
![25^{x-1}=5^{2x-1}-100\\\\=>\ (5^2)^{x-1}=5^{2x-1}\ -2^2*5^2\\\\=>\ 5^{2x-2}-5^{2x-1}\ = - 2^2*5^2\\\\=>\ 5^{2x-2}*[ 1-5^1 ]=-2^2*5^2\\\\=>\ 5^{2x-2}*-4=-4*5^2\\\\=>\ 2x-2=2\\\\x=2](https://tex.z-dn.net/?f=25%5E%7Bx-1%7D%3D5%5E%7B2x-1%7D-100%5C%5C%5C%5C%3D%26gt%3B%5C+%285%5E2%29%5E%7Bx-1%7D%3D5%5E%7B2x-1%7D%5C+-2%5E2%2A5%5E2%5C%5C%5C%5C%3D%26gt%3B%5C+5%5E%7B2x-2%7D-5%5E%7B2x-1%7D%5C+%3D+-+2%5E2%2A5%5E2%5C%5C%5C%5C%3D%26gt%3B%5C++5%5E%7B2x-2%7D%2A%5B+1-5%5E1+%5D%3D-2%5E2%2A5%5E2%5C%5C%5C%5C%3D%26gt%3B%5C++5%5E%7B2x-2%7D%2A-4%3D-4%2A5%5E2%5C%5C%5C%5C%3D%26gt%3B%5C++2x-2%3D2%5C%5C%5C%5Cx%3D2 "25^{x-1}=5^{2x-1}-100\\\\=>\ (5^2)^{x-1}=5^{2x-1}\ -2^2*5^2\\\\=>\ 5^{2x-2}-5^{2x-1}\ = - 2^2*5^2\\\\=>\ 5^{2x-2}*[ 1-5^1 ]=-2^2*5^2\\\\=>\ 5^{2x-2}*-4=-4*5^2\\\\=>\ 2x-2=2\\\\x=2")
done.
done.
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