Question

if 5 to the power 2 X + 1 divided by 25 is equal to 125 find the value of x
${5}^{2x + 1?} \div 25 = 125$

Answer 1

$\frac{ {5}^{2x + 1} }{ {5}^{2} } = {5}^{3} \\ {5}^{2x + 1 - 2} = {5}^{3} \\ 2x - 1 = 3 \\ x = 2$

Answer 2

Hi there!
Here's the answer:

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5^(2x+1) ÷ 25
=> 5^(2x+1) ÷ 5²

°•° a^m ÷ a^n = a ^(m-n)

=> 5^(2x+1-2)
= 5^(2x-1)

Given this result is 125.

=> 5^(2x-1) = 125

To find the values of x, make bases equal on either sides
Which means express 125 as 5 to the power of something.

5×5×5 = 125
=> 125 = 5³

•°• 5^(2x-1) = 5^(3).


°•° Bases are equal, powers are also equal
(or)
°•° If a^m = a^n, then m = n


Equate powers on both sides
=> 2x-1 = 3
=> 2x = 4
=> x = 2

•°• Value of x = 2.

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:)


Hope it helps