Q42. - Algebra 2

Question

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

Step-by-Step Solution

Answer

The value of $r=6$ .

Step 1. Write down the given information.

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

Step 2. Calculation.

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

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

Step 3. Conclusion.

The value of $r=6$ .