Question

Solve the given problem.
${5}^{x + 2} - {5}^{x + 1} = 20$
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Answer 1

x = 1.

Step-by-step explanation:

Given :

${5}^{x + 2} - {5}^{x + 1} = 20$

To solve :

For x.

Solution :

${5}^{x + 2} - {5}^{x + 1} = 20 \: \\ => {5}^{x} \times {5}^{2} - {5}^{x} \times 5 = 20 \\ => 25 \times {5}^{x} - 5 \times {5}^{x} = 20 \\ => {5}^{x} (25 - 5) = 20 \\ => {5}^{x} \times 20 = 20 \\ => {5}^{x} = 1 \\ => {5}^{x} = {5}^{1} \\ => x = 1$

Hence, the value of x = 1.