find for x:25^x-1^x 5^2x+1= 10^2 ^× 5 + 5^3
Answers
Answer:
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
Step-by-step explanation:
Answer:
we need to bring together the terms containing x. Then constant terms on the other side. Then simplify by performing the addition/subtraction/multiplication.
\begin{gathered}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\end{gathered}
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