Question

if 5^2x-1=25^x-1+100,find the value of 3^1+x

Answer 1

Hi,

Here is the answer for your question,

5^(2x-1) = 25^(x-1) + 100
5^(2x-1)= 5^(2x-2) + 100
5^(2x-1) - 5^(2x-2) = 100
Taking 5^(2x-1) common

5^(2x-1)[ 1-(5^-1)] = 100
5^(2x-1)[1-1/5] =100
5^(2x-1) × 4/5 = 100
5^(2x-1) ×2²/5= 2²×5². .....( Cancelling 2² both the sides )

5^(2x-1-1) = 5²
5^(2x-2) = 5²
As bases are same powers get compared
2x-2 = 2
2x = 2+2
2x=4
x= 2

Therefore , 3^(1+x) = 3^ (1+2)
= 3 ³= 27 ......


Hence, 27 is the answer


Hope it helps

Thank-you

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Answer 2

Step-by-step explanation:

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