If $25^{x - 1} = 5^{2 x - 1} - 100$ , then the value of $x$ is ____.

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $2$
$5^{2 x - 2} = 5^{2 x - 1} - 100$
shift $5^{2 x - 2}$ to the left hand side
Now, Multiply the equation with -1
$5^{2 x - 1} - 5^{2 x - 2} = 100$
$5^{2 x - 2} (5 - 1) = 100$
$5^{2 x - 2} = \frac{100}{4}$
$25^{x - 1} = 25$ ( $∵$ $5^{2 x - 2} = (5^{2})^{x - 1}$ )
now,
$x - 1 = 1$
$x = 2$

Suggest Corrections

Similar questions

25^{(x - 1)} = 5^{(2 x - 1)} - 100

Question:- If 25^x-1 = 5^2x-1 - 100, then the value of x is_____________.

A) 3

B) 2

C) 4

D) 1

5^{2 x - 1} - (25)^{x - 1} = 2500

x

5^{2 x - 1} - 25^{x - 1} = 2500.

5^{x + 1} = 25^{x - 2}

3^{x - 3} \times 2^{3 - x}

b \frac{1}{4}

b

Join BYJU'S Learning Program