Hello!
the answer is:
the correct option:
b. ![x=2.23](/tex.php?f=x=2.23)
why?
to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.
we are given the equation:
![7^{x}=77](/tex.php?f=7^{x}=77)
then, using placing logarith with base 7 on both sides of the equation, we have:
![7^{x}=77log_{7}(7^{x})=log_{7}(77)x=log_{7}(77)x=2.2322](/tex.php?f=7^{x}=77log_{7}(7^{x})=log_{7}(77)x=log_{7}(77)x=2.2322)
so, rounding the obtained result to two decimal places (nearest hundreth), we have:
![x=2.23](/tex.php?f=x=2.23)
hence, we have that the correct option:
b. ![x=2.23](/tex.php?f=x=2.23)
have a nice day!