Find the value of m so that:
"

Given: $5^{2m-1} =25^{m-1} +100 5 2m−1 =25 m−1 +100$

To do: Find the value of m.

Solution:

We know that,

$( a^{m})^{n} =a^{m\times n} (a m ) n =a m×n$

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

$5^{2m-1} -25^{m-1} =100$

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

$5^{2m-1} -5^{2\times ( m-1)} =100\ 5^{2m-1} -5^{2m-2} =100$

$\frac{5^{2m}}{5} -\frac{5^{2m}}{5^{2}} =100$

$\frac{5^{2m}}{5} -\frac{5^{2m}}{25} =100$

$\frac{5\times 5^{2m} -5^{2m}}{25} =100$

$5^{2m}( 5-1) =100\times 25\ 5^{2m}( 4) =25\times 4\times 25\ 5^{2m}$

$=5^{2} \times 5^{2}\ 5^{2m} =5^{2+2}\ 5^{2m} =5^{4}\ 2m=4\ m=2$

​ The value of m is 2.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

32 Views

Kickstart Your Career

Get certified by completing the course

Get Started