Question

please help solve this ​

Answer 1

Question :-

Solve for x -

$\rm 5^x - 5^{x-1} = 100$

Solution :-

➩ $\rm 5^x - \dfrac{5x}{5} = 100$

➩ $\rm 5^x \Big( 1 - \dfrac{1}{5} \Big) = 100$

➩ $\rm 5^x \Big( \dfrac{4}{5} \Big) = 100$

➩ $\rm 5^x = 1 \cancel 00 \times \dfrac{5}{\cancel 4}$

➩ $\rm 5^x = 25 \times 5$

➩ $\rm 5^x = 125$

➩ $\rm 5^x = 5^3$

➩ $\boxed{\rm x = 3}$

Answer 2

Question :-

Solve for x -

$\rm 5^x - 5^{x-1} = 100$

Solution :-

➩ $\rm 5^x - \dfrac{5x}{5} = 100$

➩ $\rm 5^x \Big( 1 - \dfrac{1}{5} \Big) = 100$

➩ $\rm 5^x \Big( \dfrac{4}{5} \Big) = 100$

➩ $\rm 5^x = 1 \cancel 00 \times \dfrac{5}{\cancel 4}$

➩ $\rm 5^x = 25 \times 5$

➩ $\rm 5^x = 125$

➩ $\rm 5^x = 5^3$

➩ $\boxed{\rm x = 3}$