Question

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

• A. $x=9,a=6$
• B. $x=6,a=9$
• C. $x=5,a=6$
• D. $x=4,a=1$

Answer 1

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, $x-1=5x=5+1=6x=6$

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

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