This should just about sum it up.
Thank you interent people!
$\displaystyle f(x) = -2^{x - 1} + \frac{7}{2}$.
To find the $\displaystyle x$ intercept, let $\displaystyle f(x) = 0$.
So $\displaystyle -2^{x - 1} + \frac{7}{2} = 0$
$\displaystyle 2^{x - 1} = \frac{7}{2}$
$\displaystyle 2\cdot 2^{x - 1} = 7$
$\displaystyle 2^{x} = 7$
$\displaystyle \ln{(2^x)} = \ln{7}$
$\displaystyle x\ln{2} = \ln{7}$
$\displaystyle x = \frac{\ln{7}}{\ln{2}}$.
You should know that
$\displaystyle a^m \cdot a^n = a^{m + n}$.
Here you have
$\displaystyle 2^1 \cdot 2^{x - 1} = 2^{1 + x - 1} = 2^x$.
And your teacher is wrong.
Either s/he meant $\displaystyle \frac{\ln{7}}{\ln{2}}$ or s/he meant $\displaystyle \log_2{7}$.