Question

If 5²x-1=25x-1+100; find the value of 3¹+x

Answer 1

Answer:

$5^{2x - 1}$ = $25^{x-1}$ + 100

Firstly take all the terms to the base of 5,

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

or, $5^{2x - 1}$ - $5^{2(x-1)}$ = 100

or, $\frac{5^{2x} }{5}$ - $\frac{5^{2x} }{25}$ = 100

or, $\frac{5 X 5^{2x} - 5^{2x} }{25}$ = 100

or, 5 X ($5^{2x}$)  (5-1)= 2500

or, 5 X ($5^{2x}$) = $\frac{2500}{4}$ = 625

or, ($5^{2x}$) = $\frac{625}{5}$ = 125

or, ($5^{2x}$) = $5^{3}$

from LHS and RHS,

2x = 3

or, x = 3/2

So, $3^{1+x}$ = $3^{\frac{5}{2} }$ = 9$\sqrt{3}$