If $2^{x - 1} = 2^{5} = 2^{a - 4}$ , then find the value of $x$ and $a$ .

x = 4, a = 1

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x = 6, a = 9

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x = 5, a = 6

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x = 9, a = 6

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Solution

The correct option is B $x = 6, a = 9$
Given: $2^{x - 1} = 2^{5} = 2^{a - 4}$
The bases are same. Hence, the exponents should be same.
Here, $2^{x - 1} = 2^{5}$
Then, $x - 1 = 5 x = 5 + 1 = 6 x = 6$

Similarly, $2^{5} = 2^{a - 4}$
Then, $5 = a - 4 a = 5 + 4 = 9 a = 9$

Hence, the value of $x$ is 6 and the value of $a$ is 9.

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