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Chapter 5: Q42. (page 227)

If $2^{r + 5} = 2^{2 r - 1}$ , what is the value ofr ?

Short Answer

Expert verified

The value of $r = 6$ .

Step by step solution

01

Step 1. Write down the given information.

The given expression is $2^{r + 5} = 2^{2 r - 1}$ .

02

Step 2. Calculation.

Simplifying the given expression $2^{r + 5} = 2^{2 r - 1}$ .

$\begin{matrix} 2^{r + 5} = 2^{2 r - 1} .... (Given) \\ r + 5 = 2 r - 1.... (\begin{array}{l} If x^{a} = x^{b} \\ then a = b \end{array}) \\ 2 r - r = 5 + 1 \\ r = 6 \end{matrix}$

03

Step 3. Conclusion.

The value of $r = 6$ .

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