Question

Find the value of $x$ if $5^{x-7}=1$.

• A. $x=5$
• B. $x=1$
• C. $x=6$
• D. $x=7$

Answer 1

The correct option is D $x=7$

$\underset{–}{\text{Need to find:}}$ Value of $x$ in $5^{x-7}=1$

As we know that, any non-zero number raised to the power $0$ is equal to $1$.
Hence, $1=5^0$.

$\therefore 5^{x-7}=1=5^0$
$\Rightarrow 5^{x-7}=5^0$

As in the above equation, bases are same, we can equate the exponents.

$\Rightarrow x-7=0$
$\Rightarrow x-7+7=0+7$
$\Rightarrow \underset{–}{x=7}$

The value of $x$ in the equation $5^{x-7}=1$ is $7$.

Therefore, option (d.) is the correct one.